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.

Example

Input

8 3

Output

5

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