given three integers n, m and k

/**
 * @param {number} n
 * @param {number} m
 * @param {number} k
 * @return {number}
 */
var numOfArrays = function (n, m, k) {

  const dp = new Array(51)
    .fill(null)
    .map(() => new Array(51).fill(null).map(() => new Array(101).fill(-1)));

  const MOD = 1_00_00_00_007;

  function dfs(idx, lenLIS, largest) {
    if (idx === n) {
      if (lenLIS === k) {
        return 1;
      }
      return 0;
    }

    if (dp[idx][lenLIS][largest] !== -1) {
      return dp[idx][lenLIS][largest];
    }

    let ans = 0;

    for (let i = 1; i <= m; i++) {
      if (i > largest) {
        ans += dfs(idx + 1, lenLIS + 1, i);
      } else {
        ans += dfs(idx + 1, lenLIS, largest);
      }

      ans %= MOD;
    }

    dp[idx][lenLIS][largest] = ans;
    return ans;
  }

  return dfs(0, 0, 0)
};