Beautiful Intervals

Given two integers K and N, you are required to construct N beautiful intervals [L_i, R_i] that satisfy the following conditions:

• $L_1 = 1$.
• $L_i \le R_i$ for all $i$.
• $R_i - L_i \ge K$ for all $i$.
• For any $i > 1$, $L_i = R_{i-1} + 1$.
• $\gcd(L_i, R_i) = 1$, where $\gcd$ denotes the greatest common divisor.
• Under the above conditions, the difference $R_i - L_i$ should be as small as possible for each interval.

Your task is to produce the N intervals following these requirements.

inputFormat

The input consists of a single line containing two space-separated integers K and N, where K is the minimum required difference and N is the number of intervals to construct.

outputFormat

Output N lines. Each line contains two integers L and R separated by a space, representing one beautiful interval [L, R].

sample

1 3

1 2
3 4
5 6