<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:
    void print(vector<vector<long long>>& dp){
        for(int i=0; i<dp.size(); i++){
            for(int j=0; j<dp[i].size(); j++){
                cout << dp[i][j] << " ";
            }
            cout << "\n";
        }
        cout << "\n";
    }
    int kInversePairs(int n, int k) {
        vector<vector<long long>> dp(k+1, vector<long long>(n+1));
        long long MOD = (long long)(1e9 + 7);
        dp[0][0] = 0;
        for(int i=1; i<=n; i++){
            dp[0][i] = 1;
        }
        long long ans = 1;
        for(int c=1; c<=k; c++){
            for(int i=1; i<=n; i++){
                dp[c][i] = (dp[c-1][i] + dp[c][i-1]) % MOD;
                ans = dp[c][i-1];
                if(c >= i){
                    dp[c][i] = (dp[c][i] - dp[c-i][i-1] + MOD) % MOD;
                    ans = (ans - dp[c-i][i-1] + MOD) % MOD;
                }
            }
        }
        // print(dp);

        return (int)ans;
    }
};
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