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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Linq;
using System.Text.RegularExpressions;
using System.Collections.Generic;
using static program.Input;
using static program.MyMath;
using static System.Console;

namespace program {
  class Program {
    static string alp = "abcdefghijklmnopqrstuvwxyz";
    static string Alp = "ABCDEFGHIJKLMNOPQRSTUVWXYZ";
    static long MOD = 1000000007;
    static void Main()
    {
      var HN = ScanLongArray();
      var H = HN[0];
      var N = HN[1];
      var dp = (new long[H+1]).Select(_=>100000000l).ToArray(); // HP=H, 必要MPの最小値
      var magic = new long[N];
      var damage = new long[N];
      for(int i=0; i<N; i++){
        var input = ScanLongArray();
        damage[i] = input[0];
        magic[i] = input[1];
      }
      
      dp[H] = 0;
      for(long i=H; i>=0; i--){
        for(long k=0; k<N; k++){
          var hp = Math.Max(0, i - damage[k]);
          dp[hp] = Math.Min(dp[hp], dp[i] + magic[k]);
        }
      }
      
      WriteLine(dp[0]);
    }
  }
  
  static class Input {
    static public int ScanInt() { return int.Parse(Console.ReadLine()); }
    static public uint ScanUint() { return uint.Parse(Console.ReadLine()); }
    static public double ScanDouble() { return double.Parse(Console.ReadLine()); }
    static public long ScanLong() { return long.Parse(Console.ReadLine()); }
    static public ulong ScanUlong() { return ulong.Parse(Console.ReadLine()); }
    static public int[] ScanIntArray() { return Console.ReadLine().Split().Select(x => int.Parse(x)).ToArray(); }
    static public uint[] ScanUintArray() { return Console.ReadLine().Split().Select(x => uint.Parse(x)).ToArray(); }
    static public double[] ScanDoubleArray() { return Console.ReadLine().Split().Select(x => double.Parse(x)).ToArray(); }
    static public long[] ScanLongArray() { return Console.ReadLine().Split().Select(x => long.Parse(x)).ToArray(); }
    static public ulong[] ScanUlongArray() { return Console.ReadLine().Split().Select(x => ulong.Parse(x)).ToArray(); }

    static public string ScanStr() { return Console.ReadLine(); }
    static public string[] ScanStrArray() { return ScanStr().Split(); }
    static public string RegaxReplace(this string arg1, string pattern, string replacement) { return Regex.Replace(arg1, pattern, replacement); }
    static public string Join<T>(this IEnumerable<T> source, string separator) { return string.Join(separator, source); }
  }
  
  static class MyMath {
    static public long[] CumSum(this long[] a){
      var res = new long[a.Length];
      long s=0;
      for(int i=0; i<a.Length; i++) res[i] = (s += a[i]);
      return res;
    }
    static public IEnumerable<int> PrimeFactors(this int n)
    {
      int tmp = n;
      for(int i=2; i*i <= n; i++) {
        while(tmp%i==0){
          tmp /= i;
          yield return i;
        }
      }
      if(tmp != 1) yield return tmp;
    }
    static public IEnumerable<long> PrimeFactors(this long n)
    {
      var tmp = n;
      for(long i=2; i*i <= n; i++) {
        while(tmp%i==0){
          tmp /= i;
          yield return i;
        }
      }
      if(tmp != 1) yield return tmp;
    }
    static public int Digit(this int n, int d){ if(d<0) return 0; return (n%(int)Math.Pow(10,d+1)) / (int)Math.Pow(10,d); }
  	static public int Length(this int n) { if(n<0) return 0; return (int)Math.Log10(n)+1; }
    static public int Top(this int n) { return n.Digit(n.Length()-1); }
    public static bool isPrime(this int p){
      if(p<=1) return false;
      for(int i=2; i*i<=p; i++)
        if(p%i==0) return false;
      return true;
    }
    public static bool isPrime(this long p){
      if(p<=1) return false;
      for(long i=2; i*i<=p; i++)
        if(p%i==0) return false;
      return true;
    }
    public static int GCD(int a, int b) {
        Func<int, int, int> gcd = null;
        gcd = (x, y) => y == 0 ? x : gcd(y, x % y);
        return a > b ? gcd(a, b) : gcd(b, a);
    }
    public static long GCD(long a, long b) {
        Func<long, long, long> gcd = null;
        gcd = (x, y) => y == 0 ? x : gcd(y, x % y);
        return a > b ? gcd(a, b) : gcd(b, a);
    }
    public static ulong extGCD(ulong a, ulong b, ref ulong x, ref ulong y) {
      if(b==0) {
        x=1; 
        y=0;
        return a;
      }
      var d = extGCD(b, a%b, ref y, ref x);
      y -= a/b *x;
      return d;
    }
    public static int LCM(int a, int b) { return a * b / GCD(a, b); }
    public static long LCM(long a, long b) { return a * b / GCD(a, b); }
    public static long Inv(this long a, long m = 1000000007) {
      long b = m, u = 1, v = 0;
      while (b!=0) {
        long t = a / b;
        a -= t * b;
        swap(ref a, ref b);
        u -= t * v;
        swap(ref u, ref v);
      }
      u %= m; 
      if (u < 0) u += m;
      return u;
	}
    private static void swap(ref long a, ref long b){
        var t = a;
        a = b;
        b = t;
    }
  }
}