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 $i (2 \leq i \leq N-1), 2 A_i \leq A_{i-1} + A_{i+1}$.

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.

Constraints

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

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

见题面 Input 部分

见题面 Output 部分