The More The Better

Given an sequence of numbers {X₁, X₂, ... , X_n}, where X_k = (A * k + B) % mod. Your task is to find the maximum sub sequence {Y₁, Y₂, ... , Y_m} where every pair of (Y_i, Y_j) satisfies Y_i + Y_j <= L (1 ≤ i < j ≤ m), and every Y_i <= L (1 ≤ i ≤ m ).
Now given n, L, A, B and mod, your task is to figure out the maximum m described above.

Multiple test cases, process to the end of input. Every test case has a single line. A line of 5 integers: n, L, A, B and mod. (1 ≤ n ≤ 2*10⁷, 1 ≤ L ≤ 2*10⁹, 1 ≤ A, B, mod ≤ 10⁹)

For each case, output m in one line.

1 8 2 3 6
5 8 2 3 6

1
4

2012 Multi-University Training Contest 8