Shomtring

A string made only of the characters A and B is called a Shomtring if it satisfies all of the following conditions.

• It uses at most countA characters A.
• It uses at most countB characters B.
• Every contiguous block made only of A has length at most maxA.
• Every contiguous block made only of B has length at most maxB.

Given countA, countB, maxA, and maxB, find the maximum possible length of a Shomtring.

The first line contains four integers countA, countB, maxA, and maxB. Each value is between 0 and 1,000,000, inclusive.

Print the maximum possible length of a Shomtring.