Different Differences

2000ms

524288K

Description:

An array $$$a$$$ consisting of $$$k$$$ integers is strictly increasing if $$$a_1 < a_2 < \dots < a_k$$$. For example, the arrays $$$[1, 3, 5]$$$, $$$[1, 2, 3, 4]$$$, $$$[3, 5, 6]$$$ are strictly increasing; the arrays $$$[2, 2]$$$, $$$[3, 7, 5]$$$, $$$[7, 4, 3]$$$, $$$[1, 2, 2, 3]$$$ are not.

For a strictly increasing array $$$a$$$ of $$$k$$$ elements, let's denote the characteristic as the number of different elements in the array $$$[a_2 - a_1, a_3 - a_2, \dots, a_k - a_{k-1}]$$$. For example, the characteristic of the array $$$[1, 3, 4, 7, 8]$$$ is $$$3$$$ since the array $$$[2, 1, 3, 1]$$$ contains $$$3$$$ different elements: $$$2$$$, $$$1$$$ and $$$3$$$.

You are given two integers $$$k$$$ and $$$n$$$ ($$$k \le n$$$). Construct an increasing array of $$$k$$$ integers from $$$1$$$ to $$$n$$$ with maximum possible characteristic.

Input:

The first line contains one integer $$$t$$$ ($$$1 \le t \le 819$$$) — the number of test cases.

Each test case consists of one line containing two integers $$$k$$$ and $$$n$$$ ($$$2 \le k \le n \le 40$$$).

Output:

For each test case, print $$$k$$$ integers — the elements of the strictly increasing array $$$a$$$ with the maximum possible characteristic. If there are multiple answers, print any of them.

Sample Input:

Sample Output:

1 3 4 7 8
2 4 7 12
1 2 3
1 3 4
1 2 3 4
2 4 5 6
1 2 3 5 6 7 8 11

Informação

Provedor Codeforces

Código CF1772C