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 k^{n}
total ways) to roll the dice, so the sum of the faceup 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 109 + 7.
Constraints:
1 <= n, k <= 30
1 <= target <= 1000

