<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 ll long long
#define mod 1000000007
class Solution {
public:
    // int f(int ind,int maxVal,int k){
    //     cout<<ind<<" "<<maxVal<<" "<<k<<"\n";
    //     if(ind==gn)
    //     return k==0?1:0;
    //     if(k<0)
    //         return 0;
    //     int ansr=0;
    //     ansr=maxVal*f(ind+1,maxVal,k);
    //     for(int i=maxVal+1;i<=gm;++i)
    //         ansr+=f(ind+1,i,k-1);
    //     return ansr;
    // }
    int numOfArrays(int n, int m, int lim) {
        vector<vector<vector<ll>>> dp(n+1,vector<vector<ll>> (m+1,vector<ll> (lim+1,0)));
        for(int i=0;i<=m;++i)
        dp[n][i][0]=1;
        for(int i=n-1;i>=0;--i){
            for(int j=m;j>=0;--j){
                for(int k=0;k<=lim;++k){
                    dp[i][j][k]=(j*dp[i+1][j][k])%mod;
                    if(k==0)
                    continue;
                    for(int l=j+1;l<=m;++l)
                    dp[i][j][k]=(dp[i][j][k]+dp[i+1][l][k-1])%mod;
                    
                }
            }
        }
        return dp[0][0][lim];
    }
};
17100