MIT Individual Contest 2008

Consider the hash function h(y) = a*y + b (mod m) which maps each integer to some integer between 0 and m-1. You are given x, n, c, d and are curious how many of the hash values h(x), h(x+1) ... h(x+n) land in the interval [c, d].

Input

The first line contains a positive integer t, the number of test cases (1 ≤ t ≤ 10⁵). t lines then follow, where the ith line gives the values a, b, x, n, c, d, m, space-separated, for the ith test case. All given values are non-negative. Also, 1 ≤ m ≤ 10¹⁵, c ≤ d < m, a, b < m, x+n ≤ 10¹⁵, and a*(x+n) + b ≤ 10¹⁵.

Output

For each test case in order output the number of i, 0 ≤ i ≤ n, such that c ≤ a*(x+i) + b (mod m) ≤ d in that test case, followed by a newline.

Example

Input:
2
2 3 1 3 0 1 7
1 0 0 8 0 8 9

Output:
1
9