Problem:
Score : 500 points

Problem Statement

Ibis is fighting with a monster.

The health of the monster is H.

Ibis can cast N kinds of spells. Casting the i-th spell decreases the monster's health by A_i, at the cost of B_i Magic Points.

The same spell can be cast multiple times. There is no way other than spells to decrease the monster's health.

Ibis wins when the health of the monster becomes 0 or below.

Find the minimum total Magic Points that have to be consumed before winning.

Constraints

1 \leq H \leq 10^4

1 \leq N \leq 10^3

1 \leq A_i \leq 10^4

1 \leq B_i \leq 10^4

All values in input are integers.

Input

Input is given from Standard Input in the following format:

H N
A_1 B_1
:
A_N B_N

Output

Print the minimum total Magic Points that have to be consumed before winning.

Sample Input 1

9 3
8 3
4 2
2 1

Sample Output 1

4

First, let us cast the first spell to decrease the monster's health by 8, at the cost of 3 Magic Points. The monster's health is now 1.

Then, cast the third spell to decrease the monster's health by 2, at the cost of 1 Magic Point. The monster's health is now -1.

In this way, we can win at the total cost of 4 Magic Points.

Sample Input 2

100 6
1 1
2 3
3 9
4 27
5 81
6 243

Sample Output 2

100

It is optimal to cast the first spell 100 times.

Sample Input 3

9999 10
540 7550
691 9680
700 9790
510 7150
415 5818
551 7712
587 8227
619 8671
588 8228
176 2461

Sample Output 3

139815

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Time Limit Exceeded)

import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Map;
import java.util.Set;
import java.util.TreeMap;
import java.util.Iterator;

public class Main {

	static BufferedReader reader;
	//static field here
	
	public static void main(String[] args) {
		// TODO Auto-generated method stub
		reader = new BufferedReader(new InputStreamReader(System.in));
		//code here
		String[] HN = readLine();
		int H = Integer.parseInt(HN[0]);
		int N = Integer.parseInt(HN[1]);
		Map<Float,Attack> atks = new TreeMap<>();
		for(int i=0;i<N;i++) {
			String[] t = readLine();
			int a = Integer.parseInt(t[0]);
			int m = Integer.parseInt(t[1]);
			Attack att;
			if((att = atks.get((float)a/m))!=null) {
				if(att.m>m) {
					atks.put((float)a/m,new Attack(a,m));
				}
			}else {
				atks.put((float)a/m,new Attack(a,m));
			}
			
		}
		int Nn = atks.size();
		Attack[] atk = new Attack[Nn];
		Set<Float> ks = atks.keySet();
		Iterator<Float> ki = ks.iterator();
		for(int i=0;i<Nn;i++) {
			atk[Nn-i-1] = atks.get(ki.next());
		}
		
		ArrayList<AttackNode> atkns = new ArrayList<>();
		for(int i=0;i<Nn;i++) {
			AttackNode atknt = new AttackNode(atk[i]);
			atknt.Hleft = H - atknt.atk.a;
			atknt.M = atknt.atk.m;
			atknt.parent = null;
			atkns.add(atknt);
		}
		int minM = atk[0].m*((H+atk[0].a-1)/atk[0].a);
		AttackNode minatkn = new AttackNode(atk[0]);
		AttackNode atkntt = minatkn;
		for(int i=((atk[0].a+atk[0].m-1)/atk[0].m);i>=0;i--) {
			atkntt.child = new AttackNode(atk[0]);
			atkntt.child.parent = atkntt;
			atkntt = atkntt.child;
		}
		
		while(atkns.size()>0) {
			AttackNode atkn = atkns.remove(0);
			if(atkn.Hleft<=0) {
				if(atkn.M<minM) {
					//renew
					AttackNode atkp = atkn;
					while(atkp.parent!=null) {
						atkp = atkp.parent;
					}
					minatkn = atkp;
					minM = atkn.M;
				}
			}else if(atkn.M>=minM) {
				//end
			}else {
				//generate
				AttackNode[] atknt = atkn.generateChilds(atk);
				for(int i=0;i<atknt.length;i++) {
					int Ht = atkn.Hleft - atknt[i].child.atk.a;
					int Mt = atkn.M + atknt[i].child.atk.m;
					atknt[i].child.Hleft = Ht;
					atknt[i].child.M = Mt;
					atkns.add(0,atknt[i].child);
				}
			}
		}
		print(minM);
		
		//String[] s = readLine();
		//print(num);
	}
	
	//functions here
	//note that all methods should be STATIC
	private static long gcd(long m, long n) {
	    if(m < n) return gcd(n, m);
	    if(n == 0) return m;
	    return gcd(n, m % n);
	}
	private static long lcm(long m, long n) {
	    return m * n / gcd(m, n);
	}
	private static String[] readLine(){
		try{
			return reader.readLine().split(" ");
		}catch(Exception e){
			e.printStackTrace();
			return new String[]{e.getMessage()};
		}
	}
	private static void print(Object o){
		System.out.println(o);
	}
	private static void print(){
		System.out.println();
	}
}

class Attack{
	int a;
	int m;
	
	public Attack(int a, int m){
		// TODO 自動生成されたコンストラクター・スタブ
		this.a = a;
		this.m = m;
	}
	public String toString() {
		return a+"-"+m;
	}
}

class AttackNode{
	Attack atk;
	AttackNode parent;
	AttackNode child;
	int Hleft;
	int M;
	
	public AttackNode(Attack atk){
		// TODO 自動生成されたコンストラクター・スタブ
		this.atk = atk;
		this.child = null;
	}
	public AttackNode[] generateChilds(Attack[] atks) {
		ArrayList<AttackNode> ret = new ArrayList<>();
		float c = (float)atk.a/atk.m;
		for(int i=0;i<atks.length;i++) {
			if(c*atks[i].m<atks[i].a) {continue;}
			AttackNode node = new AttackNode(atk);
			node.child = new AttackNode(atks[i]);
			node.child.parent = node;
			ret.add(node);
		}
		return ret.toArray(new AttackNode[ret.size()]);
	}
	public String toString() {
		if(parent==null) {return atk.toString();}
		else {return parent.toString()+"->"+atk.toString();}
	}
}