p01939 Ebi-chan and Integer Sequences
B: Ebi-chan and Integer Sequences-

problem

Ebi-chan likes sequences. I especially like arithmetic progressions. This time, I decided to create a sequence that meets the following conditions.

* Arithmetic progression of length n
* When the i-th element of the sequence is defined as s_i, all s_i (1 \ leq i \ leq n) are integers that satisfy 0 \ leq s_i \ leq m.



How many sequences are there that satisfy the above conditions? However, the answer can be very large, so print the remainder after dividing by 10 ^ 9 + 7.

Input format

Input is given in one line.


n m

n represents the length of the sequence.

Constraint

* 1 \ leq n \ leq 10 ^ {15}
* 0 \ leq m \ leq 10 ^ {15}



Output format

Divide the number of arithmetic progressions that satisfy the condition by 10 ^ 9 + 7 and output the remainder in one row.

Input example 1


3 9

Output example 1


50

Input example 2


10000000000 10000000000

Output example 2


999999942

Note that the input does not fit in a 32-bit integer.





Example

Input

3 9


Output

50
```python
MOD = 10**9+7

def sum(a,d,n):
    return n*(2*a+(n-1)*d)//2

def main():
    n,m = map(int,input().split())

    s = 0
    if n == 1:
        s = m+1
    else:
        s = sum(m+1,-n+1,1+m//(n-1))
        s *= 2
        s -= (m+1)

    print(s%MOD)

if __name__ == '__main__':
    main()
```