<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>

#define M  1000000007
class Solution {
public:
int solve(int i,int n,int m,int cost,int k,int maxi, vector<vector<vector<int>>>&dp){
   if(cost>k)return 0;
   if(i==n){
     if(cost==k)return 1;
     else return 0;
   }
   if(dp[i][cost][maxi]!=-1)return dp[i][cost][maxi];
   int ans=0;
   for(int j=1;j<=m;j++){
    if(j>maxi){
        ans=(ans%M+solve(i+1,n,m,cost+1,k,j,dp)%M)%M;
    }

    else ans=(ans%M +solve(i+1,n,m,cost,k,maxi,dp)%M)%M;
   
   }
    ans%=M;
   return dp[i][cost][maxi]=ans%M;
}
    int numOfArrays(int n, int m, int k) {
           vector<vector<vector<int>>>dp(n+5,vector<vector<int>>(k+5,vector<int>(m+5,-1)));
 return solve(0,n,m,0,k,0,dp);
    }
};
14000