Educational Codeforces Round 21 Problem F (Codeforces 808F) - 最小割 - 二分答案

Digital collectible card games have become very popular recently. So Vova decided to try one of these.

Vova has n cards in his collection. Each of these cards is characterised by its power pi, magic number ci and level li. Vova wants to build a deck with total power not less than k, but magic numbers may not allow him to do so — Vova can't place two cards in a deck if the sum of the magic numbers written on these cards is a prime number. Also Vova cannot use a card if its level is greater than the level of Vova's character.

At the moment Vova's character's level is 1. Help Vova to determine the minimum level he needs to reach in order to build a deck with the required total power.

Input

The first line contains two integers n and k (1 ≤ n ≤ 100, 1 ≤ k ≤ 100000).

Then n lines follow, each of these lines contains three numbers that represent the corresponding card: pi, ci and li(1 ≤ pi ≤ 1000, 1 ≤ ci ≤ 100000, 1 ≤ li ≤ n).

Output

If Vova won't be able to build a deck with required power, print  - 1. Otherwise print the minimum level Vova has to reach in order to build a deck.

Examples

input

5 8
5 5 1
1 5 4
4 6 3
1 12 4
3 12 1

output

4

input

3 7
4 4 1
5 8 2
5 3 3

output

2

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　　题目大意是说，每个物品有三个属性p，c, l，当等级大于等于l才可已使用这个物品，选出一些物品使得两两的c之和为合数且p之和大于等于k，并且其中最大的l尽可能小，求这个最小需要达到的等级，如果无解，输出-1。

　　通过最大值中的最小值可以想到二分答案，然后考虑用网络流得到最大的p值和。

　　正确建图：2017.7.11 图论测试 T2