Grammy bought a big cake. She wants to put candles on the cake to form a pretty pattern and share the cake with her friends. Each candle can be viewed as a point on the plane. The distance between two candles is considered as the Euclidean distance on the plane. Two candles cannot be placed at the same point.

For each (unordered) pair of candles , if is one of the nearest candles of , and is one of the nearest candles of , then is called a good pair.

Grammy wants to choose the positions for all candles such that each candle is in exactly good pairs. Please help Grammy to find a set of positions for the candles or report if no solutions exist.

输入描述:

The only line contains  integers  (), denoting the number of candles and the integer chosen by Grammy.

输出描述:

If the solution does not exist, output "" on a single line.

Otherwise, output "" on the first line, then output  lines, each of which contains two real numbers  (), denoting the position of a candle. If there are multiple solutions, output any.

The distance between two candles will be calculated using double-precision floating point numbers with a tolerance of . That is, if the nearest candle to a candle  has a distance of , then all candles having a distance less than or equal to  to candle  are considered as nearest candles of . Additionally, two candles having a distance less than or equal to  are considered as two candles at the same position, which should not appear in your output.

4 1

YES
0.000000000000 0.000000000000
0.000000000000 1.000000000000
2.000000000000 0.000000000000
2.000000000000 1.000000000000

4 2

YES
0.707106781187 0.000000000000
0.000000000000 0.707106781187
-0.707106781187 0.000000000000
-0.000000000000 -0.707106781187

4 3

NO