Anti-Division

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

inputFormat

input are integers.

Input

Input is given from Standard Input in the following format:

A B C D

outputFormat

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

样例

314159265358979323 846264338327950288 419716939 937510582

532105071133627368