You have d dice and each die has f faces numbered 1, 2, ..., f.
Return the number of possible ways (out of fd total ways) modulo 109 + 7 to roll the dice so the sum of the face-up numbers equals target.
Example 1:
Input: d = 1, f = 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: d = 2, f = 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: d = 2, f = 5, target = 10 Output: 1 Explanation: You throw two dice, each with 5 faces. There is only one way to get a sum of 10: 5+5.
Example 4:
Input: d = 1, f = 2, target = 3 Output: 0 Explanation: You throw one die with 2 faces. There is no way to get a sum of 3.
Example 5:
Input: d = 30, f = 30, target = 500 Output: 222616187 Explanation: The answer must be returned modulo 10^9 + 7.
Constraints:
1 <= d, f <= 301 <= target <= 1000