<p>For an integer array <code>nums</code>, an <strong>inverse pair</strong> is a pair of integers <code>[i, j]</code> where <code>0 &lt;= i &lt; j &lt; nums.length</code> and <code>nums[i] &gt; nums[j]</code>.</p>

<p>Given two integers n and k, return the number of different arrays consisting of numbers from <code>1</code> to <code>n</code> such that there are exactly <code>k</code> <strong>inverse pairs</strong>. Since the answer can be huge, return it <strong>modulo</strong> <code>10<sup>9</sup> + 7</code>.</p>

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

<pre>
<strong>Input:</strong> n = 3, k = 0
<strong>Output:</strong> 1
<strong>Explanation:</strong> Only the array [1,2,3] which consists of numbers from 1 to 3 has exactly 0 inverse pairs.
</pre>

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

<pre>
<strong>Input:</strong> n = 3, k = 1
<strong>Output:</strong> 2
<strong>Explanation:</strong> The array [1,3,2] and [2,1,3] have exactly 1 inverse pair.
</pre>

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

<ul>
	<li><code>1 &lt;= n &lt;= 1000</code></li>
	<li><code>0 &lt;= k &lt;= 1000</code></li>
</ul>

class Solution {
public:
    int mod = (int)(1e9 + 7);
    
    int f(int n, int k, vector<vector<int>>& dp){
        
        if ( k <= 0 ) return k==0;
    
        if ( n <= 0 ) return 0;
        
        if ( dp[n][k] != -1 ) return dp[n][k];
    
        dp[n][k] = ( f ( n-1, k, dp ) + f ( n, k-1, dp ) ) % mod;
        
        return dp[n][k] = ( dp[n][k] - f ( n-1, k-n, dp ) + mod ) % mod;

    }
    int kInversePairs(int n, int k) {
        
        vector<vector<int>> dp(n+1,vector<int>(k+1,-1));

        return f(n,k,dp);

    }
};
23800