# Poisoned Dagger solution codeforces

Monocarp is playing yet another computer game. In this game, his character has to kill a dragon. The battle with the dragon lasts 100500100500 seconds, during which Monocarp attacks the dragon with a poisoned dagger. The 𝑖i-th attack is performed at the beginning of the 𝑎𝑖ai-th second from the battle start. The dagger itself does not deal damage, but it applies a poison effect on the dragon, which deals 11 damage during each of the next 𝑘k seconds (starting with the same second when the dragon was stabbed by the dagger). However, if the dragon has already been poisoned, then the dagger updates the poison effect (i.e. cancels the current poison effect and applies a new one).

For example, suppose 𝑘=4k=4, and Monocarp stabs the dragon during the seconds 2244 and 1010. Then the poison effect is applied at the start of the 22-nd second and deals 11 damage during the 22-nd and 33-rd seconds; then, at the beginning of the 44-th second, the poison effect is reapplied, so it deals exactly 11 damage during the seconds 445566 and 77; then, during the 1010-th second, the poison effect is applied again, and it deals 11 damage during the seconds 101011111212 and 1313. In total, the dragon receives 1010 damage.

Monocarp knows that the dragon has h hit points, and if he deals at least h damage to the dragon during the battle — he slays the dragon. Monocarp has not decided on the strength of the poison he will use during the battle, so he wants to find the minimum possible value of 𝑘k (the number of seconds the poison effect lasts) that is enough to deal at least h damage to the dragon.

Input Poisoned Dagger solution codeforces

The first line contains a single integer 𝑡t (1𝑡10001≤t≤1000) — the number of test cases.

The first line of the test case contains two integers 𝑛n and h (1𝑛100;110181≤n≤100;1≤h≤1018) — the number of Monocarp’s attacks and the amount of damage that needs to be dealt.

The second line contains 𝑛n integers 𝑎1a1𝑎2a2, …, 𝑎𝑛an (1𝑎𝑖109;𝑎𝑖<𝑎𝑖+11≤ai≤109;ai<ai+1), where 𝑎𝑖ai is the second when the 𝑖i-th attack is performed.

Output

For each test case, print a single integer — the minimum value of the parameter 𝑘k, such that Monocarp will cause at least h damage to the dragon.

Example Poisoned Dagger solution codeforces

input

Copy
4
2 5
1 5
3 10
2 4 10
5 3
1 2 4 5 7
4 1000
3 25 64 1337


output Poisoned Dagger solution codeforces

Copy
3
4
1
470

Note

In the first example, for 𝑘=3k=3, damage is dealt in seconds [1,2,3,5,6,7][1,2,3,5,6,7].

In the second example, for 𝑘=4k=4, damage is dealt in seconds [2,3,4,5,6,7,10,11,12,13][2,3,4,5,6,7,10,11,12,13].

In the third example, for 𝑘=1k=1, damage is dealt in seconds [1,2,4,5,7][1,2,4,5,7].

[Solution] MEX Sequences solution codeforces