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10 초 512 MB 3 3 3 100.000%

문제

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 wi and length li, for 1 ≤ i ≤ 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.

입력

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 wi and length li of each piece.

Limits

  • 1 ≤ N ≤ 5 000 000;
  • 1 ≤ W, L ≤ 10 000;
  • for each 1 ≤ i ≤ N, 1 ≤ wi, li ≤ 10 000.

출력

The output should be the integer L.

예제 입력 1

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

예제 출력 1

6

힌트