You are given four integers A, B, C, and D. Find the number of integers between A and B (inclusive) that can be evenly divided by neither C nor D.

Constraints

* 1\leq A\leq B\leq 10^{18}
* 1\leq C,D\leq 10^9
* All values in input are integers.

Input

Input is given from Standard Input in the following format:


A B C D


Output

Print the number of integers between A and B (inclusive) that can be evenly divided by neither C nor D.

Examples

Input

4 9 2 3


Output

2


Input

10 40 6 8


Output

23


Input

314159265358979323 846264338327950288 419716939 937510582


Output

532105071133627368
#!/usr/bin/env python

from collections import deque
import itertools as ite
import sys
import math

sys.setrecursionlimit(1000000)

INF = 10 ** 18
MOD = 10 ** 9 + 7

A, B, C, D = map(int, raw_input().split())
def GCD(a, b):
	dummy1 = max(a, b)
	dummy2 = min(a, b)
	while True:
		dummy = dummy1 % dummy2
		dummy1 = dummy2
		dummy2 = dummy
		if dummy == 0:
			break
	return dummy1

ans = 0

LCM = C * D / GCD(C, D)

ans += B
ans -= B / D
ans -= B / C
ans += B / LCM
A -= 1
ans -= A
ans += A / D
ans += A / C
ans -= A / LCM
print ans