Knapsack 2

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.

Examples

Input

3 8 3 30 4 50 5 60

Output

90

Input

1 1000000000 1000000000 10

Output

10

Input

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

Output

17

inputFormat

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

outputFormat

Output

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

Examples

Input

3 8 3 30 4 50 5 60

Output

90

Input

1 1000000000 1000000000 10

Output

10

Input

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

Output

17

样例

1 1000000000
1000000000 10

10