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

inputFormat

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}

outputFormat

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

样例

3 9

50