Problem:
Score : 100 points

Problem Statement

There are N items, numbered 1, 2, \ldots, N.
For each i (1 \leq i \leq N), Item i has a weight of w_i and a value of v_i.

Taro has decided to choose some of the N items and carry them home in a knapsack.
The capacity of the knapsack is W, which means that the sum of the weights of items taken must be at most W.

Find the maximum possible sum of the values of items that Taro takes home.

Constraints

All values in input are integers.

1 \leq N \leq 100

1 \leq W \leq 10^9

1 \leq w_i \leq W

1 \leq v_i \leq 10^3

Input

Input is given from Standard Input in the following format:

N W
w_1 v_1
w_2 v_2
:
w_N v_N

Output

Print the maximum possible sum of the values of items that Taro takes home.

Sample Input 1

3 8
3 30
4 50
5 60

Sample Output 1

90

Items 1 and 3 should be taken.
Then, the sum of the weights is 3 + 5 = 8, and the sum of the values is 30 + 60 = 90.

Sample Input 2

1 1000000000
1000000000 10

Sample Output 2

10

Sample Input 3

6 15
6 5
5 6
6 4
6 6
3 5
7 2

Sample Output 3

17

Items 2, 4 and 5 should be taken.
Then, the sum of the weights is 5 + 6 + 3 = 14, and the sum of the values is 6 + 6 + 5 = 17.

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;
using static program.Const;

namespace program
{
  class Program
  {
    static void Main()
    {
      var input = ScanIntArray();
      var n = input[0];
      var w = input[1];
      // Valueをiにするために必要な最小の重さ
      var dp = new long[100001].Select(_=>(long)INF).ToArray();
      dp[0] = 0;
      for(int i=0; i<n; i++) {
        var h = ScanLongArray(); // w,v
        for(long k=100000; k>=h[1]; k--){
          dp[k] = Math.Min(dp[k],dp[k-h[1]]+h[0]);
        }
      }
      for(long k=100000; k>=0; k--){
        if(dp[k] <= w){
          WriteLine(k); return;
        }
      }
    }
  }

  static class Const
  {
    public static string alp = "abcdefghijklmnopqrstuvwxyz";
    public static string Alp = "ABCDEFGHIJKLMNOPQRSTUVWXYZ";
    public static long MOD = 1000000007;
    public static int INF = int.MaxValue;
    public static long INFL = long.MaxValue;
  }
  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 int Floor2(this int a)
    {
      int N = 1;
      while (N < a) N *= 2;
      return N / 2;
    }
    static public long Floor2(this long a)
    {
      long N = 1;
      while (N < a) N *= 2;
      return N / 2;
    }
    static public int Ceiling2(this int a)
    {
      int N = 1;
      while (N < a) N *= 2;
      return N;
    }
    static public long Ceiling2(this long a)
    {
      long N = 1;
      while (N < a) N *= 2;
      return N;
    }
    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;
    }
  }


}