<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:
    long long int MOD=1000000007;
    int solveUsingRecursion(int n,int k,int target,int diceUsed,int currSum){
        if(diceUsed==n && currSum==target){
            return 1;
        }
        if(diceUsed==n && currSum!=target){
            return 0;
        }
        if(currSum==target && diceUsed!=n){
            return 0;
        }
        int ans=0;
        for(int face=1;face<=k;face++){
            ans=ans+solveUsingRecursion(n,k,target,diceUsed+1,currSum+face);
        }
        return ans;
}

     int solveUsingMem(int n,int k,int target,int diceUsed,int currSum,vector<vector<int>>&dp){
        if(diceUsed==n && currSum==target){
            return 1;
        }
        if(diceUsed==n && currSum!=target){
            return 0;
        }
        if(currSum==target && diceUsed!=n){
            return 0;
        }
        if(dp[diceUsed][currSum]!=-1){
            return dp[diceUsed][currSum];
        }
        int ans=0;
        for(int face=1;face<=k;face++){
            int recAns=0;
            if(currSum+face<=target){
               recAns=solveUsingMem(n,k,target,diceUsed+1,currSum+face,dp);
            }
            ans=(ans%MOD+recAns%MOD)%MOD;
        }
        dp[diceUsed][currSum]=ans;
        return dp[diceUsed][currSum];
}

    int solveUsingTabulation(int n,int k,int target){
        vector<vector<int>>dp(n+1,vector<int>(target+1,0));
        dp[n][target]=1;
        for(int dice=n-1;dice>=0;dice--){
            for(int sum=target;sum>=0;sum--){
                int ans=0;
               for(int face=1;face<=k;face++){
                 int recAns=0;
                 if(sum+face<=target){
               recAns=dp[dice+1][sum+face];
            }
            ans=(ans%MOD+recAns%MOD)%MOD;
        }
        dp[dice][sum]=ans; 
            }
        }
        return dp[0][0];
    }

    int solveUsingTabulationSO(int n,int k,int target){
        vector<int>curr(target+1,0);
        vector<int>next(target+1,0);
        next[target]=1;
        for(int dice=n-1;dice>=0;dice--){
            for(int sum=target;sum>=0;sum--){
                int ans=0;
               for(int face=1;face<=k;face++){
                 int recAns=0;
                 if(sum+face<=target){
               recAns=next[sum+face];
            }
            ans=(ans%MOD+recAns%MOD)%MOD;
        }
        curr[sum]=ans; 
            }
            next=curr;
        }
        return next[0];
    }

    int numRollsToTarget(int n, int k, int target) {
        int diceUsed=0;
        int currSum=0;
        // vector<vector<int>>dp(n+1,vector<int>(target+1,-1));
        int ans=solveUsingTabulationSO(n,k,target);
        return ans;
    }
};
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