Statement

This question is based on bonus of this problem.

We need to count such triple $$$(a, b, c)$$$ that satisfy $$$(0 \leq a + b + c \leq S)$$$ and $$$(0 \leq a \times b \times c \leq T)$$$ and $$$min(a, b, c) \geq 0$$$

Since this number may be very big, let take the result modulo $$$10^9 + 7$$$

Notice that:

• $$$(0, 0, 1) \neq (0, 1, 0) \neq (1, 0, 0)$$$

Constraint:

• $$$0 \leq S, T \leq 10^{18}$$$

• $$$0 \leq a, b, c$$$

Time Limit: 1s

Memory Limit: 1Gb

Input:

• A single line contain only two positive 60-bit integers $$$S$$$ and $$$T$$$ ($$$0 \leq S, T \leq 10^18$$$)

Output:

• Print a single integer, the number of positive tuple satisfy mathematical condition, modulo $$$1000000007$$$

Example

Input:
0 0

Output:
1

Explain:
(0, 0, 0)

Input:
1 1

Output:
4

Explain:
(0, 0, 0)
(0, 0, 1)
(0, 1, 0)
(1, 0, 0)

Input:
10 10

Output:
213

Input:
100 100

Output:
16616

Input:
1000 1000

Output:
1530920

Input:
10000 10000

Output:
150511618

Input:
100000 100000

Output:
2122766957