<p>You are given three integers <code>n</code>, <code>m</code> and <code>k</code>. Consider the following algorithm to find the maximum element of an array of positive integers:</p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/04/02/e.png" style="width: 424px; height: 372px;" />
<p>You should build the array arr which has the following properties:</p>

<ul>
	<li><code>arr</code> has exactly <code>n</code> integers.</li>
	<li><code>1 &lt;= arr[i] &lt;= m</code> where <code>(0 &lt;= i &lt; n)</code>.</li>
	<li>After applying the mentioned algorithm to <code>arr</code>, the value <code>search_cost</code> is equal to <code>k</code>.</li>
</ul>

<p>Return <em>the number of ways</em> to build the array <code>arr</code> under the mentioned conditions. As the answer may grow large, the answer <strong>must be</strong> computed modulo <code>10<sup>9</sup> + 7</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> n = 2, m = 3, k = 1
<strong>Output:</strong> 6
<strong>Explanation:</strong> The possible arrays are [1, 1], [2, 1], [2, 2], [3, 1], [3, 2] [3, 3]
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> n = 5, m = 2, k = 3
<strong>Output:</strong> 0
<strong>Explanation:</strong> There are no possible arrays that satisfy the mentioned conditions.
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> n = 9, m = 1, k = 1
<strong>Output:</strong> 1
<strong>Explanation:</strong> The only possible array is [1, 1, 1, 1, 1, 1, 1, 1, 1]
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= n &lt;= 50</code></li>
	<li><code>1 &lt;= m &lt;= 100</code></li>
	<li><code>0 &lt;= k &lt;= n</code></li>
</ul>

class Solution {
public:
    int generate(const int &n, const int &m, const int &k, int i, int score, int maxVal)
    {
        if (i == n)
        {
            if (score == k)
            {
                return 1;
            }
            return 0;
        }
        int answer = 0;
        int mV = 0;
        for (int j = 1; j <= m; ++j)
        {
            mV = max(maxVal, j);
            if ((score + (j > maxVal)) <= k)
            {
                if (hash[i + 1][score + (j > maxVal)][mV] == INT_MIN)
                {
                    hash[i + 1][score + (j > maxVal)][mV] = generate(n, m, k, i + 1, score + (j > maxVal), mV)% 1000000007;
                }
                answer = (answer + hash[i + 1][score + (j > maxVal)][mV]) % 1000000007;
            }
        }
        return answer;
    }
    int numOfArrays(int n, int m, int k) {
        hash.resize(n + 1, vector<vector<int>>(k + 1, vector<int>(m + 1, INT_MIN)));
        return generate(n, m, k, 0, 0, INT_MIN);
    }
private:
    vector<vector<vector<int>>> hash;
};
12200