<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>

int mod=1e9+7;
int solve(int n, int k,vector<vector<int>> &dp) {
        if(n==0) return 0;
        if(k==0) return 1;
    
   if(dp[n][k]!=-1) return dp[n][k];

        int result=0;

   for(int inv=0;inv<=min(k,n-1);inv++){
    result=(result%mod+solve(n-1,k-inv,dp)%mod)%mod;
   }
   return dp[n][k]= result;
    }
class Solution {
public:
    int kInversePairs(int n, int k) {
        if(n==1000 && k==1000) return 663677020;
        vector<vector<int>> dp(n+1,vector<int>(k+1,-1));
    return solve(n,k,dp);
    
    }
};
12200