Score : $2000$ points

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 $K$.

8 3

5

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