Problem Statement

Given are integers $N$ and $M$. Find the number, modulo $(10^9+7)$, of length-$N$ sequences $(A_1,A_2,\\ldots,A_N)$ that consist of non-negative integers and satisfy the following conditions:

• $A_1+A_2+\\ldots +A_N = M$;
• For every $i$ ($2 \\leq i \\leq N-1$), $2 A_i \\leq A_{i-1} + A_{i+1}$.

Constraints

• $1 \\leq N \\leq 10^5$
• $1 \\leq M \\leq 10^5$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$ $M$

Output

Print the number, modulo $(10^9+7)$, of sequences that satisfy the conditions.

Sample Input 1

3 3

Sample Output 1

7

The following seven sequences satisfy the conditions.

• $0,0,3$
• $0,1,2$
• $1,0,2$
• $1,1,1$
• $2,0,1$
• $2,1,0$
• $3,0,0$

Sample Input 2

10 100

Sample Output 2

10804516

Sample Input 3

10000 100000

Sample Output 3

694681734