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}~

Input

Input is given from Standard Input in the following format:

~R~ ~B~

Output

Print the maximum possible value of ~K~ .

Sample Input 1

8 3

Sample Output 1

5

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