One day, Ahmed_Hossam went to Hemose and said “Let’s solve a gym contest!”. Hemose didn’t want to do that, as he was playing Valorant, so he came up with a problem and told it to Ahmed to distract him. Sadly, Ahmed can’t solve it… Could you help him? There is an Agent in Valorant, and he has nn weapons. The ii-th weapon has a damage value aiai, and the Agent will face an enemy whose health value is HH.

Gamer Hemose solution codeforces

One day, Ahmed_Hossam went to Hemose and said “Let’s solve a gym contest!”. Hemose didn’t want to do that, as he was playing Valorant, so he came up with a problem and told it to Ahmed to distract him. Sadly, Ahmed can’t solve it… Could you help him?

There is an Agent in Valorant, and he has nn weapons. The ii-th weapon has a damage value aiai, and the Agent will face an enemy whose health value is HH.

The Agent will perform one or more moves until the enemy dies.

In one move, he will choose a weapon and decrease the enemy’s health by its damage value. The enemy will die when his health will become less than or equal to 00. However, not everything is so easy: the Agent can’t choose the same weapon for 22 times in a row.

What is the minimum number of times that the Agent will need to use the weapons to kill the enemy?

 Gamer Hemose solution codeforces

Each test contains multiple test cases. The first line contains the number of test cases tt (1t105)(1≤t≤105). Description of the test cases follows.

The first line of each test case contains two integers nn and HH (2n103,1H109)(2≤n≤103,1≤H≤109) — the number of available weapons and the initial health value of the enemy.

The second line of each test case contains nn integers a1,a2,,ana1,a2,…,an (1ai109)(1≤ai≤109) — the damage values of the weapons.

It’s guaranteed that the sum of nn over all test cases doesn’t exceed 21052⋅105.

 Gamer Hemose solution codeforces

For each test case, print a single integer — the minimum number of times that the Agent will have to use the weapons to kill the enemy.

Example

input

 Gamer Hemose solution codeforces

3
2 4
3 7
2 6
4 2
3 11
2 1 7

output

Copy
1
2
3

 Gamer Hemose solution codeforces

In the first test case, the Agent can use the second weapon, making health value of the enemy equal to 47=34−7=−330−3≤0, so the enemy is dead, and using weapon 11 time was enough.

In the second test case, the Agent can use the first weapon first, and then the second one. After this, the health of enemy will drop to 642=06−4−2=0, meaning he would be killed after using weapons 22 times.

In the third test case, the Agent can use the weapons in order (third, first, third), decreasing the health value of enemy to 11727=511−7−2−7=−5 after using the weapons 33 times. Note that we can’t kill the enemy by using the third weapon twice, as even though 1177<011−7−7<0, it’s not allowed to use the same weapon twice in a row.

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