Candies

There are N children, numbered 1, 2, \ldots, N.

They have decided to share K candies among themselves. Here, for each i (1 \leq i \leq N), Child i must receive between 0 and a_i candies (inclusive). Also, no candies should be left over.

Find the number of ways for them to share candies, modulo 10^9 + 7. Here, two ways are said to be different when there exists a child who receives a different number of candies.

Constraints

• All values in input are integers.
• 1 \leq N \leq 100
• 0 \leq K \leq 10^5
• 0 \leq a_i \leq K

Input

Input is given from Standard Input in the following format:

N K a_1 a_2 \ldots a_N

Output

Print the number of ways for the children to share candies, modulo 10^9 + 7.

Examples

Input

3 4 1 2 3

Output

5

Input

1 10 9

Output

0

Input

2 0 0 0

Output

1

Input

4 100000 100000 100000 100000 100000

Output

665683269

inputFormat

input are integers.

• 1 \leq N \leq 100
• 0 \leq K \leq 10^5
• 0 \leq a_i \leq K

Input

Input is given from Standard Input in the following format:

N K a_1 a_2 \ldots a_N

outputFormat

Output

Print the number of ways for the children to share candies, modulo 10^9 + 7.

Examples

Input

3 4 1 2 3

Output

5

Input

1 10 9

Output

0

Input

2 0 0 0

Output

1

Input

4 100000 100000 100000 100000 100000

Output

665683269

样例

2 0
0 0

1