You are given two integers N and D.

Find N six-sided dice with faces labelled with nonnegative integers not more than 10^6 such that:

• for each die, the six numbers written on its faces are all distinct, and
• if you roll all dice, the bitwise XOR of the N numbers on top is always divisible by D.

Under the given constraints, it can be shown that a solution always exists.

Input Format

The only line contains the two integers N and D.

Output Format

Output N lines, the i-th of which contains six distinct space-separated nonnegative integers at most 10^6 — the faces of the i-th die.

If there are multiple possible answers, output any of them.

Constraints

• 1 ≤ N ≤ 100
• 2 ≤ D ≤ 60

Sample 0

Input

3 2

Output

1 3 5 7 9 11
3 5 7 9 11 2023
0 2 4 6 1000000 10

Explanation

There are three dice:

• Die 1 has faces [1, 3, 5, 7, 9, 11].
• Die 2 has faces [3, 5, 7, 9, 11, 2023].
• Die 3 has faces [0, 2, 4, 6, 1000000, 10].

Suppose we rolled the dice, and they landed on 7, 3, and 2. Then their bitwise XOR is 7 ⊕ 3 ⊕ 2 = 6, which is a multiple of 2.