Numbers for Two Groups

Medium

An organizer hands out numbers to the members of two groups. The numbers are positive integers. - Group A needs count_a distinct numbers, none of them divisible by skip_a. - Group B needs count_b distinct numbers, none of them divisible by skip_b. - No number may be given to both groups. Return the smallest possible value of the largest number handed out.

Example 1

skip_a=3, skip_b=2, count_a=2, count_b=2 → 4

Group A gets 2 and 4 (not multiples of 3) and group B gets 1 and 3 (odd). The largest number is 4.

Example 2

skip_a=2, skip_b=2, count_a=3, count_b=1 → 7

Both groups can only use odd numbers, and four distinct ones are needed: 1, 3, 5 and 7. So 7 cannot be avoided.

Constraints

2 ≤ skip_a, skip_b ≤ 10⁵
1 ≤ count_a, count_b < 10⁹
2 ≤ count_a + count_b ≤ 10⁹

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Topics

Math Binary Search Number Theory

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Input

skip_a=3, skip_b=2, count_a=2, count_b=2

Expected

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