You are going from City A to City B. The distance between A and B is \(S\) km. In the most days, you can go at most \(X\) km one day. But there are \(N\) exceptions, in the \(T_i\) th day, you can go at most \(Y_i\) km. You need to find out the minimum number of days required to reach city $$B$$ from city $$A$$.

Input Format

First line contains three integers, \(S,X,N (1\le S,X\le 10^9,0\le N\le 10^3)\).

The \((i+1)\) th line contains two integers \(T_i,Y_i(1\le T_i,Y_i\le 10^9)\).

It's guaranteed any two \(T_i\) are different. Note that \(T_i\) is not sorted.

Output Format

One integer represents the answer.