# 1155 Number of Dice Rolls With Target Sum

You have `n` dice, and each die has `k` faces numbered from `1` to `k`.

Given three integers `n`, `k`, and `target`, return the number of possible ways (out of the `kn` total ways) to roll the dice, so the sum of the face-up numbers equals `target`. Since the answer may be too large, return it modulo `109 + 7`.

Example 1:

``````Input: n = 1, k = 6, target = 3
Output: 1
Explanation: You throw one die with 6 faces.
There is only one way to get a sum of 3.
``````

Example 2:

``````Input: n = 2, k = 6, target = 7
Output: 6
Explanation: 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.
``````

Example 3:

``````Input: n = 30, k = 30, target = 500
Output: 222616187
Explanation: The answer must be returned modulo 109 + 7.
``````

Constraints:

• `1 <= n, k <= 30`
• `1 <= target <= 1000`
 `````` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 `````` ``````class Solution: def numRollsToTarget(self, n: int, k: int, target: int) -> int: MOD = 10 ** 9 + 7 dp = [[0] * (target + 1) for _ in range(2)] for i in range(1, min(k, target)+1): dp[0][i] = 1 for i in range(1, n): r = i % 2 p = (i-1) % 2 for j in range(i-1, target+1): # start from (i-1) since impossible to get sum # of j < i with i dices current = 0 for l in range(max(1, j - k), j): current += dp[p][l] dp[r][j] = current return dp[(n-1) % 2][-1] % MOD``````