You are given three integers n, m and k. Consider the following algorithm to find the maximum element of an array of positive integers:
![\"\"](\"https://assets.leetcode.com/uploads/2020/04/02/e.png\")
\nYou should build the array arr which has the following properties:
\n\narr has exactly n integers.1 <= arr[i] <= m where (0 <= i < n).arr, the value search_cost is equal to k.Return the number of ways to build the array arr under the mentioned conditions. As the answer may grow large, the answer must be computed modulo 109 + 7.
\n
Example 1:
\n\n\nInput: n = 2, m = 3, k = 1\nOutput: 6\nExplanation: The possible arrays are [1, 1], [2, 1], [2, 2], [3, 1], [3, 2] [3, 3]\n\n\n
Example 2:
\n\n\nInput: n = 5, m = 2, k = 3\nOutput: 0\nExplanation: There are no possible arrays that satisfy the mentioned conditions.\n\n\n
Example 3:
\n\n\nInput: n = 9, m = 1, k = 1\nOutput: 1\nExplanation: The only possible array is [1, 1, 1, 1, 1, 1, 1, 1, 1]\n\n\n
\n
Constraints:
\n\n1 <= n <= 501 <= m <= 1000 <= k <= nCompiled with clang 11 using the latest C++ 20 standard.
Your code is compiled with level two optimization (-O2). AddressSanitizer is also enabled to help detect out-of-bounds and use-after-free bugs.
Most standard library headers are already included automatically for your convenience.
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Some common data structure implementations are provided in the Algorithms module: https://www.rubydoc.info/github/kanwei/algorithms/Algorithms
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