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 Rust (1.15.1) (judge verdict: Wrong Answer)

#![allow(non_snake_case)]

use std::cmp;

#[allow(dead_code)]
pub struct Scanner<'a> {
    _buf: &'a str,
    iter: ::std::str::SplitWhitespace<'a>,
}

#[allow(dead_code)]
impl<'a> Scanner<'a> {
    pub fn new(buf: &'a str) -> Self {
        Scanner {
            _buf: buf,
            iter: buf.split_whitespace(),
        }
    }

    pub fn array<T>(&mut self, n: usize) -> Vec<T>
        where T: ::std::str::FromStr,
              T::Err: ::std::fmt::Debug,
    {
        let mut res = Vec::with_capacity(n);
        for _ in 0..n {
            res.push(self.value());
        }
        res
    }

    pub fn value<T>(&mut self) -> T
        where T: ::std::str::FromStr,
              T::Err: ::std::fmt::Debug,
    {
        self.next().parse().unwrap()
    }

    pub fn chars(&mut self) -> Vec<char> {
        self.next().chars().collect()
    }

    fn next(&mut self) -> &str {
        self.iter.next().unwrap()
    }
}

const INF: i64 = 1_010_000_000_000_000_000;

struct Solver {
    W: Vec<i64>,
    V: Vec<i64>,
    memo: Vec<Vec<Option<i64>>>,
}

impl Solver {
    fn new(W: Vec<i64>, V: Vec<i64>) -> Self {
        Solver {
            W: W,
            V: V,
            memo: vec![vec![None; 100001]; 101],
        }
    }

    /// i 個までで価値 j を実現する最小の重さ(不可能なら INF)
    fn f(&mut self, i: i64, j: i64) -> i64 {
        if i == 0 && j == 0 { return 0; }
        if i == 0 {
            return if j == self.V[0] { self.W[0] } else { INF };
        }

        if self.memo[i as usize][j as usize].is_none() {
            let w = self.W[(i-1) as usize];
            let v = self.V[(i-1) as usize];

            let mut res = self.f(i-1,j);
            if v <= j {
                res = cmp::min(res, w + self.f(i-1,j-v));
            }
            self.memo[i as usize][j as usize] = Some(res);
        }
        self.memo[i as usize][j as usize].unwrap()
    }
}

fn main() {
    let mut _input = String::new();
    {
        use ::std::io::Read;
        ::std::io::stdin().read_to_string(&mut _input).unwrap();
    }
    let mut sc = Scanner::new(&_input);

    let N    = sc.value::<i64>();
    let WMAX = sc.value::<i64>();
    let mut W = Vec::with_capacity(N as usize);
    let mut V = Vec::with_capacity(N as usize);
    for _ in 0..N {
        W.push(sc.value::<i64>());
        V.push(sc.value::<i64>());
    }

    let mut sol = Solver::new(W, V);
    let mut ans = 0;
    for j in 0..100001 {
        if sol.f(N,j) <= WMAX {
            ans = j;
        }
    }

    println!("{}", ans);
}