Problem C
Cable Car

At $3147.3$ meters high, Fansipan is the tallest mountain in the Indochina peninsula. To promote tourism, $n$ stations were built on the mountain, numbered from $1$ to $n$.

Two companies, Mobi and Vina are in charge of operating cable cars connecting the stations. Each of the two companies have $k$ cable cars. The $i$-th cable car of Mobi connects two stations $M{S}_i$ and $M{E}_i$. The $i$-th cable car of Vina connects two stations $V{S}_i$ and $V{E}_i$.

Two stations are called connected by a company, iff we can go from one station to the other by using cable cars only of that company. To achieve peaceful cooperation, the two companies agreed with the following conditions:

• For every valid $i$, $M{S}_i<M{E}_i$ and $V{S}_i<V{E}_i$.

• All $M{S}_i$ are unique, all $M{E}_i$ are unique.

• All $V{S}_i$ are unique, all $V{E}_i$ are unique.

• For any $i\ne j$, if $M{S}_i<M{S}_j$, then $M{E}_i<M{E}_j$.

• For any $i\ne j$, if $V{S}_i<V{S}_j$, then $V{E}_i<V{E}_j$.

• No pair of stations is connected by both companies. In other words, for every pair of stations $i$ and $j$, if $i$ and $j$ are connected by Mobi, they should not be connected by Vina, and vice versa.

Given $n$ and $k$, your task is to check whether it is possible for Mobi and Vina to each operates $k$ cable cars, satisfying all the above conditions.

Input

The input contains two integers $n$ and $k$, separated by a single space $(1\le k<n\le 100)$.

Output

For each test case, if it is not possible to satisfy all the conditions, print ‘NO’. Otherwise, print ‘YES’, followed by $2\cdot k$ lines. In the first $k$ lines, the $i$-th line contains two integers $M{S}_i$ and $M{E}_i$. In the last $k$ lines, the $i$-th line contains two integers $V{S}_i$ and $V{E}_i$.

3 1

YES
1 2
1 3

3 2

NO