710_D. Two Arithmetic Progressions
Problem Description
You are given two arithmetic progressions: a1k + b1 and a2l + b2. Find the number of integers x such that L ≤ x ≤ R and x = a1k' + b1 = a2l' + b2, for some integers k', l' ≥ 0.
Input
The only line contains six integers a1, b1, a2, b2, L, R (0 < a1, a2 ≤ 2·109, - 2·109 ≤ b1, b2, L, R ≤ 2·109, L ≤ R).
Output
Print the desired number of integers x.
Examples
Input
2 0 3 3 5 21
Output
3
Input
2 4 3 0 6 17
Output
2
Contest Information
- Contest ID: 710
- Problem Index: D
- Points: 0.0
- Rating: 2500
- Tags: math, number theory
- Time Limit: {'seconds': 1, 'nanos': 0} seconds
- Memory Limit: 256000000 bytes
Task
Solve this competitive programming problem. Provide a complete solution that handles all the given constraints and edge cases.