Number of Dice Rolls With Target Sum
You have n dice, and each dice has k faces numbered from 1 to k.
You have n dice, and each dice 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 10^9 + 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 10^9 + 7.
Constraints
- 1 <= n, k <= 30
- 1 <= target <= 1000
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