Problem C
Shattered Cake


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 into $N$ perfectly rectangular pieces of width $w_ i$ and length $l_ i$, for $1\leqslant i\leqslant N$.

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.


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.


  • $1\leqslant N\leqslant 5\, 000\, 000$;

  • $1\leqslant W,L \leqslant 10\, 000$;

  • for each $1\leq i\leq N$, $1\leqslant w_ i,l_ i \leqslant 10\, 000$.


The output should be the integer $L$.

Sample Input 1 Sample Output 1
2 3
1 4
1 2
1 2
2 2
2 2
2 1

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