题目描述

A rectangular cake is transported via a truck to a restaurant. On the way to the destination, the truck hits a pothole, which shatters the cake in $N$ perfectly rectangular pieces of width $w_i$ and length $l_i$, for $1 \leq i \leq N$.

At the destination, the damage is assessed, and the customer decides to order a replacement cake of the same dimensions. Unfortunately, the original order form was incompletely filled and only the width $W$ of the cake is known. The restaurant asks for your help to find out the length $L$ of the cake. Fortunately, all pieces of the shattered cake have been kept.

输入格式

The input consists of the following integers:

• on the first line, the width $W$ of the cake;
• on the second line, the number $N$ of shattered pieces;
• on each of the next $N$ lines, the width $w_i$ and length $l_i$ of each piece.

输出格式

The output should be the integer $L$.

4
7
2 3
1 4
1 2
1 2
2 2
2 2
2 1

6

提示

Limits

• $1 \leq N \leq 5\,000\,000$;
• $1 \leq W, L \leq 10\,000$;
• for each $1 \leq i \leq N$, $1 \leq w_i, l_i \leq 10\,000$.