<p>You have <code>n</code> dice, and each dice has <code>k</code> faces numbered from <code>1</code> to <code>k</code>.</p>

<p>Given three integers <code>n</code>, <code>k</code>, and <code>target</code>, return <em>the number of possible ways (out of the </em><code>k<sup>n</sup></code><em> total ways) </em><em>to roll the dice, so the sum of the face-up numbers equals </em><code>target</code>. Since the answer may be too large, 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 = 1, k = 6, target = 3
<strong>Output:</strong> 1
<strong>Explanation:</strong> You throw one die with 6 faces.
There is only one way to get a sum of 3.
</pre>

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

<pre>
<strong>Input:</strong> n = 2, k = 6, target = 7
<strong>Output:</strong> 6
<strong>Explanation:</strong> You throw two dice, each with 6 faces.
There are 6 ways to get a sum of 7: 1+6, 2+5, 3+4, 4+3, 5+2, 6+1.
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> n = 30, k = 30, target = 500
<strong>Output:</strong> 222616187
<strong>Explanation:</strong> The answer must be returned modulo 10<sup>9</sup> + 7.
</pre>

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

<ul>
	<li><code>1 &lt;= n, k &lt;= 30</code></li>
	<li><code>1 &lt;= target &lt;= 1000</code></li>
</ul>

class Solution {
public:
int val =1000000007;
    int solve(int d, int k, int target, vector<vector<int>>&dp){
        if(d==0 && target==0)
        return 1;
        if(d==0 || target<=0)
        return 0;
        if(dp[d][target]!=-1)
        return dp[d][target]%val;
        int c=0;
        for(int i =1;i<=k;i++){
         c=(c+solve(d-1,k,target-i,dp))%val;
        }
        dp[d][target]=c%val;
        return dp[d][target];

    }
    int numRollsToTarget(int n, int k, int target) {
       vector<vector<int>>dp;
       int i,j;
       for(i=0;i<=n;i++){
        vector<int>v;
        for(j=0;j<=target;j++){
            v.push_back(-1);
        }
        dp.push_back(v);
       } 
       return solve(n,k,target,dp);
    }
};
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