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 PyPy3 (2.4.0) (judge verdict: Accepted)



N, W = map(int, input().split())
wv = [tuple(map(int, input().split())) for _ in range(N)]

INF = float("inf")
"""
Wの最大が大きすぎるのでふつうのDPはできない
総重量W以下で、価値Vを得るときの最小重さをDPで求める感じ
"""

dp = [{} for _ in range(N+1)]
#何も選ばないときの価値が０で重さが０で初期化。忘れない
dp[0][0] = 0

for i,(w,v) in enumerate(wv):
    for v_sum,w_sum in dp[i].items():

        # i番目の品について考えるとき、i-1までに同じ価値の品があるなら軽いほうを選択、ないならi番目を選択
        if v_sum in dp[i+1]:
            dp[i+1][v_sum] = min(dp[i+1][v_sum], w_sum)
        else:
            dp[i+1][v_sum] = w_sum

        # i-1番目までで起こりえる組み合わせとi番目を選んだ場合に制限を超えるなら飛ばす
        if w + w_sum > W: continue

        # i-1番目までで起こりえる組み合わせとi番目を選んだ場合に、その価値の組み合わせがすでにあるなら軽いほうを、ないならその組み合わせの重さを保存
        if v + v_sum in dp[i+1]:
            dp[i+1][v+v_sum] = min(dp[i+1][v+v_sum], w + w_sum)
        else:
            dp[i+1][v+v_sum] = w + w_sum

#print(dp)
print(max(dp[N].keys()))