<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>

vector<vector<int>> dp;

class Solution {
    const int mod=1000000007;
public:
    int kInversePairs(int n, int k) {
        if (dp.size()==0) {
            dp=vector<vector<int>>(1005, vector<int>(2005, 0));
            dp[1][0]=1;
            dp[1][1]=-1;
            for (int i=1; i<1001; ++i) {
                for (int j=1; j<1001; ++j) {
                    dp[i][j]=(dp[i][j]+dp[i][j-1])%mod;
                }
                for (int j=0; j<1001; ++j) {
                    dp[i+1][j]=(dp[i+1][j]+dp[i][j])%mod;
                    dp[i+1][i+j+1]=(dp[i+1][i+j+1]-dp[i][j])%mod;
                }
            }
        }
        return (dp[n][k]+mod)%mod;
    }
};
18900