write a go solution for Description:
The king of Berland organizes a ball! n pair are invited to the ball, they are numbered from 1 to n. Each pair consists of one man and one woman. Each dancer (either man or woman) has a monochrome costume. The color of each costume is represented by an integer from 1 to k, inclusive.

Let b_i be the color of the man's costume and g_i be the color of the woman's costume in the i-th pair. You have to choose a color for each dancer's costume (i.e. values b_1,b_2,...,b_n and g_1,g_2,...g_n) in such a way that:

1. for every i: b_i and g_i are integers between 1 and k, inclusive;
2. there are no two completely identical pairs, i.e. no two indices i,j (inej) such that b_i=b_j and g_i=g_j at the same time;
3. there is no pair such that the color of the man's costume is the same as the color of the woman's costume in this pair, i.e. b_ineg_i for every i;
4. for each two consecutive (adjacent) pairs both man's costume colors and woman's costume colors differ, i.e. for every i from 1 to n-1 the conditions b_ineb_i+1 and g_ineg_i+1 hold.

Let's take a look at the examples of bad and good color choosing (for n=4 and k=3, man is the first in a pair and woman is the second):

Bad color choosing:

- (1,2), (2,3), (3,2), (1,2) — contradiction with the second rule (there are equal pairs);
- (2,3), (1,1), (3,2), (1,3) — contradiction with the third rule (there is a pair with costumes of the same color);
- (1,2), (2,3), (1,3), (2,1) — contradiction with the fourth rule (there are two consecutive pairs such that colors of costumes of men/women are the same).

Good color choosing:

- (1,2), (2,1), (1,3), (3,1);
- (1,2), (3,1), (2,3), (3,2);
- (3,1), (1,2), (2,3), (3,2).

You have to find any suitable color choosing or say that no suitable choosing exists.

Input Format:
The only line of the input contains two integers n and k (2<=n,k<=2*10^5) — the number of pairs and the number of colors.

Output Format:
If it is impossible to find any suitable colors choosing, print "NO".

Otherwise print "YES" and then the colors of the costumes of pairs in the next n lines. The i-th line should contain two integers b_i and g_i — colors of costumes of man and woman in the i-th pair, respectively.

You can print each letter in any case (upper or lower). For example, "YeS", "no" and "yES" are all acceptable.

Note:
None. Output only the code with no comments, explanation, or additional text.