Problem Statement

Snuke has R red balls and B blue balls. He distributes them into K boxes, so that no box is empty and no two boxes are identical. Compute the maximum possible value of K.

Formally speaking, let's number the boxes 1 through K. If Box i contains r_i red balls and b_i blue balls, the following conditions must be satisfied:

• For each i (1 \leq i \leq K), r_i > 0 or b_i > 0.
• For each i, j (1 \leq i < j \leq K), r_i \neq r_j or b_i \neq b_j.
• \sum r_i = R and \sum b_i = B (no balls can be left outside the boxes).

Constraints

• 1 \leq R, B \leq 10^{9}

Sample Input 1

8 3

Sample Output 1

5

The following picture shows one possible way to achieve K = 5: