# 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

```java
```