How many arrays $A$ of length $n$ consisting of non-negative integers do not exceed $k$ such that the sum of every 2 adjacent elements is a prime number?
### Input
- The first line contains 2 integers $n, k$.
### Output
- Print the number of satisfied array modulo $10^9+7$.
### Constraints
- $1 \le n \le 100$
- $1 \le k \le 1000$.
### Example
Input:
```
2 2
```
Output:
```
5
```
#### Note: There are $5$ arrays: $(0, 2), (1, 1), (1, 2), (2, 1), (2, 0)$.
