public class Solution
extends Object
1155 - Number of Dice Rolls With Target Sum\.
Medium
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`