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        "answer": "def count_beautiful_integers(low: int, high: int, k: int) -> int:\n    \"\"\" Count the number of beautiful integers in the range [low, high].\n    \n    A number is beautiful if it meets both conditions:\n    1. The count of even digits equals the count of odd digits\n    2. The number is divisible by k\n    \n    Args:\n        low: Lower bound of the range (inclusive), 0 < low <= high <= 10^9\n        high: Upper bound of the range (inclusive)\n        k: Divisor to check, 0 < k <= 20\n    \n    Returns:\n        The count of beautiful integers in the given range\n    \n    >>> count_beautiful_integers(10, 20, 3)\n    2\n    >>> count_beautiful_integers(1, 10, 1)\n    1\n    >>> count_beautiful_integers(5, 5, 2)\n    0\n    \"\"\"\n\n    def count_upto(n: int) -> int:\n        if n <= 0:\n            return 0\n        digits = list(map(int, str(n)))\n        L = len(digits)\n        from functools import lru_cache\n\n        @lru_cache(maxsize=None)\n        def dp(pos, balance, mod, started, tight):\n            if pos == L:\n                if not started:\n                    # the number 0 itself (not a positive integer)\n                    return 0\n                return 1 if (balance == 0 and mod == 0) else 0\n            limit = digits[pos] if tight else 9\n            total = 0\n            for d in range(limit + 1):\n                ntight = tight and (d == limit)\n                if not started and d == 0:\n                    total += dp(pos + 1, balance, mod, False, ntight)\n                else:\n                    if d % 2 == 0:\n                        nb = balance + 1\n                    else:\n                        nb = balance - 1\n                    nmod = (mod * 10 + d) % k\n                    total += dp(pos + 1, nb, nmod, True, ntight)\n            return total\n\n        return dp(0, 0, 0, False, True)\n\n    return count_upto(high) - count_upto(low - 1)\n",
        "explanation": "All tests passed!\nAll tests passed!\n",
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            "func.py": "def count_beautiful_integers(low: int, high: int, k: int) -> int:\n    \"\"\" Count the number of beautiful integers in the range [low, high].\n    \n    A number is beautiful if it meets both conditions:\n    1. The count of even digits equals the count of odd digits\n    2. The number is divisible by k\n    \n    Args:\n        low: Lower bound of the range (inclusive), 0 < low <= high <= 10^9\n        high: Upper bound of the range (inclusive)\n        k: Divisor to check, 0 < k <= 20\n    \n    Returns:\n        The count of beautiful integers in the given range\n    \n    >>> count_beautiful_integers(10, 20, 3)\n    2\n    >>> count_beautiful_integers(1, 10, 1)\n    1\n    >>> count_beautiful_integers(5, 5, 2)\n    0\n    \"\"\"\n\n    def count_upto(n: int) -> int:\n        if n <= 0:\n            return 0\n        digits = list(map(int, str(n)))\n        L = len(digits)\n        from functools import lru_cache\n\n        @lru_cache(maxsize=None)\n        def dp(pos, balance, mod, started, tight):\n            if pos == L:\n                if not started:\n                    # the number 0 itself (not a positive integer)\n                    return 0\n                return 1 if (balance == 0 and mod == 0) else 0\n            limit = digits[pos] if tight else 9\n            total = 0\n            for d in range(limit + 1):\n                ntight = tight and (d == limit)\n                if not started and d == 0:\n                    total += dp(pos + 1, balance, mod, False, ntight)\n                else:\n                    if d % 2 == 0:\n                        nb = balance + 1\n                    else:\n                        nb = balance - 1\n                    nmod = (mod * 10 + d) % k\n                    total += dp(pos + 1, nb, nmod, True, ntight)\n            return total\n\n        return dp(0, 0, 0, False, True)\n\n    return count_upto(high) - count_upto(low - 1)\n",
            "test.py": "from func import count_beautiful_integers\n\ndef test_func(candidate):\n    # Example test cases\n    assert candidate(10, 20, 3) == 2\n    assert candidate(1, 10, 1) == 1\n    assert candidate(5, 5, 2) == 0\n    \n    # Additional test cases\n    assert candidate(1, 1, 1) == 0\n    assert candidate(19, 50, 2) == 6\n    assert candidate(94, 94, 9) == 0\n    assert candidate(94, 100, 1) == 3\n    assert candidate(52, 396, 9) == 5\n    assert candidate(47, 735, 2) == 15\n    assert candidate(90, 110, 16) == 1\n    assert candidate(934, 991, 1) == 0\n    assert candidate(1, 1000000000, 1) == 24894045\n    assert candidate(33340762, 612987024, 1) == 18196584\n    assert candidate(36954768, 642296821, 14) == 1240042\n    assert candidate(17946863, 807558969, 17) == 1319380\n\nif __name__ == \"__main__\":\n    test_func(count_beautiful_integers)\n    print(\"All tests passed!\")\n"
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      "score": {
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        "answer": "def count_beautiful_integers(low: int, high: int, k: int) -> int:\n    \"\"\" Count the number of beautiful integers in the range [low, high].\n    \n    A number is beautiful if it meets both conditions:\n    1. The count of even digits equals the count of odd digits\n    2. The number is divisible by k\n    \n    Args:\n        low: Lower bound of the range (inclusive), 0 < low <= high <= 10^9\n        high: Upper bound of the range (inclusive)\n        k: Divisor to check, 0 < k <= 20\n    \n    Returns:\n        The count of beautiful integers in the given range\n    \n    >>> count_beautiful_integers(10, 20, 3)\n    2\n    >>> count_beautiful_integers(1, 10, 1)\n    1\n    >>> count_beautiful_integers(5, 5, 2)\n    0\n    \"\"\"\n\n    def count_upto(n: int) -> int:\n        if n <= 0:\n            return 0\n        digits = list(map(int, str(n)))\n        L = len(digits)\n        from functools import lru_cache\n\n        @lru_cache(maxsize=None)\n        def dp(pos, balance, mod, started, tight):\n            if pos == L:\n                if not started:\n                    # the number 0 itself (not a positive integer)\n                    return 0\n                return 1 if (balance == 0 and mod == 0) else 0\n            limit = digits[pos] if tight else 9\n            total = 0\n            for d in range(limit + 1):\n                ntight = tight and (d == limit)\n                if not started and d == 0:\n                    total += dp(pos + 1, balance, mod, False, ntight)\n                else:\n                    if d % 2 == 0:\n                        nb = balance + 1\n                    else:\n                        nb = balance - 1\n                    nmod = (mod * 10 + d) % k\n                    total += dp(pos + 1, nb, nmod, True, ntight)\n            return total\n\n        return dp(0, 0, 0, False, True)\n\n    return count_upto(high) - count_upto(low - 1)\n",
        "explanation": "All tests passed!\nAll tests passed!\n",
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            "func.py": "def count_beautiful_integers(low: int, high: int, k: int) -> int:\n    \"\"\" Count the number of beautiful integers in the range [low, high].\n    \n    A number is beautiful if it meets both conditions:\n    1. The count of even digits equals the count of odd digits\n    2. The number is divisible by k\n    \n    Args:\n        low: Lower bound of the range (inclusive), 0 < low <= high <= 10^9\n        high: Upper bound of the range (inclusive)\n        k: Divisor to check, 0 < k <= 20\n    \n    Returns:\n        The count of beautiful integers in the given range\n    \n    >>> count_beautiful_integers(10, 20, 3)\n    2\n    >>> count_beautiful_integers(1, 10, 1)\n    1\n    >>> count_beautiful_integers(5, 5, 2)\n    0\n    \"\"\"\n\n    def count_upto(n: int) -> int:\n        if n <= 0:\n            return 0\n        digits = list(map(int, str(n)))\n        L = len(digits)\n        from functools import lru_cache\n\n        @lru_cache(maxsize=None)\n        def dp(pos, balance, mod, started, tight):\n            if pos == L:\n                if not started:\n                    # the number 0 itself (not a positive integer)\n                    return 0\n                return 1 if (balance == 0 and mod == 0) else 0\n            limit = digits[pos] if tight else 9\n            total = 0\n            for d in range(limit + 1):\n                ntight = tight and (d == limit)\n                if not started and d == 0:\n                    total += dp(pos + 1, balance, mod, False, ntight)\n                else:\n                    if d % 2 == 0:\n                        nb = balance + 1\n                    else:\n                        nb = balance - 1\n                    nmod = (mod * 10 + d) % k\n                    total += dp(pos + 1, nb, nmod, True, ntight)\n            return total\n\n        return dp(0, 0, 0, False, True)\n\n    return count_upto(high) - count_upto(low - 1)\n",
            "test.py": "from func import count_beautiful_integers\n\ndef test_func(candidate):\n    # Example test cases\n    assert candidate(10, 20, 3) == 2\n    assert candidate(1, 10, 1) == 1\n    assert candidate(5, 5, 2) == 0\n    \n    # Additional test cases\n    assert candidate(1, 1, 1) == 0\n    assert candidate(19, 50, 2) == 6\n    assert candidate(94, 94, 9) == 0\n    assert candidate(94, 100, 1) == 3\n    assert candidate(52, 396, 9) == 5\n    assert candidate(47, 735, 2) == 15\n    assert candidate(90, 110, 16) == 1\n    assert candidate(934, 991, 1) == 0\n    assert candidate(1, 1000000000, 1) == 24894045\n    assert candidate(33340762, 612987024, 1) == 18196584\n    assert candidate(36954768, 642296821, 14) == 1240042\n    assert candidate(17946863, 807558969, 17) == 1319380\n\nif __name__ == \"__main__\":\n    test_func(count_beautiful_integers)\n    print(\"All tests passed!\")\n"
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      "answer": "def count_beautiful_integers(low: int, high: int, k: int) -> int:\n    \"\"\" Count the number of beautiful integers in the range [low, high].\n    \n    A number is beautiful if it meets both conditions:\n    1. The count of even digits equals the count of odd digits\n    2. The number is divisible by k\n    \n    Args:\n        low: Lower bound of the range (inclusive), 0 < low <= high <= 10^9\n        high: Upper bound of the range (inclusive)\n        k: Divisor to check, 0 < k <= 20\n    \n    Returns:\n        The count of beautiful integers in the given range\n    \n    >>> count_beautiful_integers(10, 20, 3)\n    2\n    >>> count_beautiful_integers(1, 10, 1)\n    1\n    >>> count_beautiful_integers(5, 5, 2)\n    0\n    \"\"\"\n\n    def count_upto(n: int) -> int:\n        if n <= 0:\n            return 0\n        digits = list(map(int, str(n)))\n        L = len(digits)\n        from functools import lru_cache\n\n        @lru_cache(maxsize=None)\n        def dp(pos, balance, mod, started, tight):\n            if pos == L:\n                if not started:\n                    # the number 0 itself (not a positive integer)\n                    return 0\n                return 1 if (balance == 0 and mod == 0) else 0\n            limit = digits[pos] if tight else 9\n            total = 0\n            for d in range(limit + 1):\n                ntight = tight and (d == limit)\n                if not started and d == 0:\n                    total += dp(pos + 1, balance, mod, False, ntight)\n                else:\n                    if d % 2 == 0:\n                        nb = balance + 1\n                    else:\n                        nb = balance - 1\n                    nmod = (mod * 10 + d) % k\n                    total += dp(pos + 1, nb, nmod, True, ntight)\n            return total\n\n        return dp(0, 0, 0, False, True)\n\n    return count_upto(high) - count_upto(low - 1)\n",
      "explanation": "All tests passed!\nAll tests passed!\n",
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          "func.py": "def count_beautiful_integers(low: int, high: int, k: int) -> int:\n    \"\"\" Count the number of beautiful integers in the range [low, high].\n    \n    A number is beautiful if it meets both conditions:\n    1. The count of even digits equals the count of odd digits\n    2. The number is divisible by k\n    \n    Args:\n        low: Lower bound of the range (inclusive), 0 < low <= high <= 10^9\n        high: Upper bound of the range (inclusive)\n        k: Divisor to check, 0 < k <= 20\n    \n    Returns:\n        The count of beautiful integers in the given range\n    \n    >>> count_beautiful_integers(10, 20, 3)\n    2\n    >>> count_beautiful_integers(1, 10, 1)\n    1\n    >>> count_beautiful_integers(5, 5, 2)\n    0\n    \"\"\"\n\n    def count_upto(n: int) -> int:\n        if n <= 0:\n            return 0\n        digits = list(map(int, str(n)))\n        L = len(digits)\n        from functools import lru_cache\n\n        @lru_cache(maxsize=None)\n        def dp(pos, balance, mod, started, tight):\n            if pos == L:\n                if not started:\n                    # the number 0 itself (not a positive integer)\n                    return 0\n                return 1 if (balance == 0 and mod == 0) else 0\n            limit = digits[pos] if tight else 9\n            total = 0\n            for d in range(limit + 1):\n                ntight = tight and (d == limit)\n                if not started and d == 0:\n                    total += dp(pos + 1, balance, mod, False, ntight)\n                else:\n                    if d % 2 == 0:\n                        nb = balance + 1\n                    else:\n                        nb = balance - 1\n                    nmod = (mod * 10 + d) % k\n                    total += dp(pos + 1, nb, nmod, True, ntight)\n            return total\n\n        return dp(0, 0, 0, False, True)\n\n    return count_upto(high) - count_upto(low - 1)\n",
          "test.py": "from func import count_beautiful_integers\n\ndef test_func(candidate):\n    # Example test cases\n    assert candidate(10, 20, 3) == 2\n    assert candidate(1, 10, 1) == 1\n    assert candidate(5, 5, 2) == 0\n    \n    # Additional test cases\n    assert candidate(1, 1, 1) == 0\n    assert candidate(19, 50, 2) == 6\n    assert candidate(94, 94, 9) == 0\n    assert candidate(94, 100, 1) == 3\n    assert candidate(52, 396, 9) == 5\n    assert candidate(47, 735, 2) == 15\n    assert candidate(90, 110, 16) == 1\n    assert candidate(934, 991, 1) == 0\n    assert candidate(1, 1000000000, 1) == 24894045\n    assert candidate(33340762, 612987024, 1) == 18196584\n    assert candidate(36954768, 642296821, 14) == 1240042\n    assert candidate(17946863, 807558969, 17) == 1319380\n\nif __name__ == \"__main__\":\n    test_func(count_beautiful_integers)\n    print(\"All tests passed!\")\n"
        },
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