CodeForces - 1118E Yet Another Ball Problem 构造

The king of Berland organizes a ball! nn pair are invited to the ball, they are numbered from 11 to nn. 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 11 to kk, inclusive.

Let bibi be the color of the man's costume and gigi be the color of the woman's costume in the ii-th pair. You have to choose a color for each dancer's costume (i.e. values b1,b2,…,bnb1,b2,…,bn and g1,g2,…gng1,g2,…gn) in such a way that:

1. for every ii: bibi and gigi are integers between 11 and kk, inclusive;
2. there are no two completely identical pairs, i.e. no two indices i,ji,j (i≠ji≠j) such that bi=bjbi=bj and gi=gjgi=gj 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. bi≠gibi≠gi for every ii;
4. for each two consecutive (adjacent) pairs both man's costume colors and woman's costume colors differ, i.e. for every ii from 11 to n−1n−1 the conditions bi≠bi+1bi≠bi+1and gi≠gi+1gi≠gi+1 hold.

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

Bad color choosing:

• (1,2)(1,2), (2,3)(2,3), (3,2)(3,2), (1,2)(1,2) — contradiction with the second rule (there are equal pairs);
• (2,3)(2,3), (1,1)(1,1), (3,2)(3,2), (1,3)(1,3) — contradiction with the third rule (there is a pair with costumes of the same color);
• (1,2)(1,2), (2,3)(2,3), (1,3)(1,3), (2,1)(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)(1,2), (2,1)(2,1), (1,3)(1,3), (3,1)(3,1);
• (1,2)(1,2), (3,1)(3,1), (2,3)(2,3), (3,2)(3,2);
• (3,1)(3,1), (1,2)(1,2), (2,3)(2,3), (3,2)(3,2).

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

Input

The only line of the input contains two integers nn and kk (2≤n,k≤2⋅1052≤n,k≤2⋅105) — the number of pairs and the number of colors.

Output

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 nnlines. The ii-th line should contain two integers bibi and gigi — colors of costumes of man and woman in the ii-th pair, respectively.

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

Examples

Input

4 3

Output

YES
3 1
1 3
3 2
2 3

Input

10 4

Output

YES
2 1
1 3
4 2
3 4
4 3
3 2
2 4
4 1
1 4
3 1

Input

13 4

Output

NO

题意：题目大意，要求构造一个(ai, bi)序列，ab的值在[1, k]内，要求同一个(ai, bi)内aibi不能相同，相邻的两个ai或bi不能相同，所有的a或b不能相同，没有两个完全一样的(ai, bi)。

题解：就是个傻逼题，题目中都给你最简单的构造方式了，就是按顺序枚举两个即可，一共k*(k-1) 种

#include
using namespace std;
typedef long long ll;
ll n,m;
int main()
{
	cin>>n>>m;
	if(m*(m-1)=n)
			{
				return 0;
			}
			cout<=n)
			{
				return 0;
			}
		}
	}
	return 0;
}