Get Optimal String Length

Using at most countA A's and countB B's, with at most maxA consecutive A's and at most maxB consecutive B's, find the maximum length of a string you can construct. You need not use all the characters; a maximum run length of 0 for a letter means that letter cannot be used.

输入格式

One line containing countA countB maxA maxB, all four integers in 0..10^6.

输出格式

Output one integer, the answer.

样例 1

输入：

5 1 2 1

输出：

5

样例 2

输入：

3 4 0 2

输出：

2

样例 3

输入：

0 0 0 0

输出：

0

样例说明

The examples give 5, 2 and 0 respectively. In the first example, AABAA can be constructed.