1155. Number of Dice Rolls With Target Sum
https://leetcode.com/problems/number-of-dice-rolls-with-target-sum
Description
You have d
dice and each die has f
faces numbered 1, 2, ..., f
. You are given three integers d
, f
, and target
.
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 <= 30
1 <= target <= 1000
ac
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