ldq's brewery

Time Limit: 1000 ms Memory Limit: 65536 KiB

Problem Description

LDQ has a black heart brewery, and in order to get people to buy a beer, he designs that a bottle of wine could just pour seven cups. Since we often have a toast at the party, we have to fill each other with a toast.

 

When there are two people , there will have three rounds, exactly one more cup, When there are three people, there will have two rounds, exactly one more cup; and four people will have three more cups.

 

In the above case, in order to obey the principle of not wasting, you will buy a bottle of beer and do another round. Of course, there's probably a lot beer to buy... Then the cycle repeats and drinks a lot. Until the beer has just finished.

 

Now LDQ has designed that the bottle could just pour the x cup, please find two people, three people, and until n people at the party, how many bottles of beer each brewery can sell .

Input

There are several sets of test data.

First line contains an integer T, which indicates the number of test cases.

Then t lines follow, each of these lines contain two integers x and n.  ( 1<=x<=10^6, 2<=n<=10^6 )

Output

For every test case, you should output n-1 lines, which respectively indicates the number of beer bottles when 2,3,4,......,n people that take part in the party could sell. 

Sample Input

1
7 5

Sample Output

2
3
4
5

Hint

Source

axuhongbo