You are given an NxM chessboard. Find the number of pairs of different positions of a bishop and a PQ-knight where they don't attack each other modulo 10^9 + 7.

A bishop can move to square if it's on the same diagonal with it.

A PQ-knight with given integers P and Q (P doesn't equals Q) can move to the square if the move forms "L-shape": P squares vertically and Q squares horizontally, or Q squares horizontally and P squares vertically. Note that if P = 1 and Q = 2, or P = 2 and Q = 1 it's a usual chess knight.

Input
The only line of the input contains 4 space-separated integers: N, M, P, Q

Output
Output one integer - the answer for the question modulo 10^9 + 7.

Constraints
0 < N, M, P, Q ≤ 10^9, P never equals Q.
N, M ≤ 30 in 40% of the test data.
N, M ≤ 10^6 in 65% of the test data.

SAMPLE INPUT
2 5 1 2

SAMPLE OUTPUT
62

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