Graph Theory#3074

Graph Theory

1 second

256 megabytes

Very easy

Serge is studying graph theory. Recently, he has learned about graph radius and diameter. Consider an undirected, unweighted, connected graph $G$ . Let us denote the length of the shortest path between vertices $s$ and $t$ as $ρ (s, t)$ . The radius $r (G)$ of the graph is defined as

r (G) = v \in V min u \in V max ρ (v, u)

r(G) = \min_{v \in V} \max_{u \in V} \rho(v, u)

The diameter $d (G)$ of the graph is defined as

d (G) = v, u \in V max ρ (v, u)

d(G) = \max_{v, u \in V} \rho(v, u)

Intuitively, the diameter of the graph is the largest distance that you need to traverse to get from one vertex to another, and the radius is the largest distance you can be forced to go from your chosen central vertex.

The professor proved during the lecture that $\frac{d ( G )}{2} \leq r (G) \leq d (G)$ \frac{d(G)}{2} \leq r(G) \leq d(G) for any graph $G$ . Now Serge wonders whether for any values $d$ and $r$ such that $\frac{d}{2} \leq r \leq d$ \frac{d}{2} \leq r \leq d, there exists a graph $G$ such that $d (G) = d$ d(G) = d and $r (G) = r$ r(G) = r. Help him to find out.

Input

The input contains two integer numbers $d$ and $r$ ( $\frac{d}{2} \leq r \leq d \leq 50$ \frac{d}{2} \leq r \leq d \leq 50, $1 \leq r$ 1 \leq r).

Output

If there exists a graph with the given radius and diameter, output YES on the first line. The second line must contain two integer numbers: $n$ ( $2 \leq n \leq 400$ 2 \leq n \leq 400) and $m$ — the number of vertices and the number of edges. The following $m$ lines must each contain two integer numbers — the vertices connected by the corresponding edge. The graph must not contain loops or parallel edges.

If there is no such graph, output NO on the first line.

Examples

Example

4 2

Example

3 1

NO

Example 1