<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 mod=1e9+7;
        long long int solve(int n,int&k,int target,vector<vector<long long int>>&dp){
           if(n<=0){
            if(target==0){
                return 1;
            }
            if(target>0||target<0){
                return 0;
            }
           }
           if(target<=0){
            return 0;
           }
           if(dp[n][target]!=-1){
            return dp[n][target];
           }
             long long int ans=0;
           for(int i=1;i<=k;i++){
             ans+=(solve(n-1,k,target-i,dp))%mod;
           }
           return dp[n][target]=ans;
         }

       long long int tab(int n,int k,int target){
         vector<vector<long long int>>dp(n+2,vector<long long int>(target+2,0));
         dp[0][0]=1;

         for(int i=1;i<=n;i++){
            for(int j=1;j<=target;j++){
               long long int ans=0;
             for(int f=1;f<=k;f++){
                if(j-f>=0)
                  ans+=(dp[i-1][j-f])%mod;
               }
               dp[i][j]=ans;
            }
         }
         return dp[n][target];
      }

    int numRollsToTarget(int n, int k, int target) {
        vector<vector<long long int>>dp(n+1,vector<long long int>(target+1,-1));
        return tab(n,k,target)%mod;
    }
};
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