You are given three integers n, d and k.

Your task is to construct an undirected tree on n vertices with diameter d and degree of each vertex at most k, or say that it is impossible.

An undirected tree is a connected undirected graph with n - 1 edges.

Diameter of a tree is the maximum length of a simple path (a path in which each vertex appears at most once) between all pairs of vertices of this tree.

Degree of a vertex is the number of edges incident to this vertex (i.e. for a vertex u it is the number of edges (u, v) that belong to the tree, where v is any other vertex of a tree).

Input

The first line of the input contains three integers n, d and k (1 ≤ n, d, k ≤ 4 ⋅ 10^5).

Output

If there is no tree satisfying the conditions above, print only one word "NO" (without quotes).

Otherwise in the first line print "YES" (without quotes), and then print n - 1 lines describing edges of a tree satisfying the conditions above. Vertices of the tree must be numbered from 1 to n. You can print edges and vertices connected by an edge in any order. If there are multiple answers, print any of them.1

Examples

Input

6 3 3


Output

YES
3 1
4 1
1 2
5 2
2 6


Input

6 2 3


Output

NO


Input

10 4 3


Output

YES
2 9
2 10
10 3
3 1
6 10
8 2
4 3
5 6
6 7


Input

8 5 3


Output

YES
2 5
7 2
3 7
3 1
1 6
8 7
4 3
import sys
input = sys.stdin.buffer.readline

from collections import deque

n,d,k=map(int,input().split())

if d>=n:
    print("NO")
    exit()

graph=[[] for i in range(n+1)]

for i in range(1,d+2):
    graph[i].append(min(i-1,d+1-i))

# print(graph)

for i in range(1,d+1):
    graph[i].append(i+1)
    graph[i+1].append(i)
# print(graph)

deg=[0]*(n+1)
deg[1]=1
deg[d+1]=1
for i in range(2,d+1):
    deg[i]=2
# print(deg)
for i in deg:
    if i>k:
        print("NO")
        exit()

p=d+2
for i in range(1,d+2):
    q=deque()
    q.append(i)
    while len(q)!=0:
        x=q.popleft()
        while (graph[x][0]>0 and deg[x]<k and p<=n):
            graph[x].append(p)
            deg[x]=deg[x]+1
            graph[p].append(graph[x][0]-1)
            graph[p].append(x)
            deg[p]=deg[p]+1
            q.append(p)
            p=p+1
    # print(graph)        

if p<=n:
    print("NO")
else:
    print("YES")  
    vis=[-1]*(n+1)

    for i in range(1,d+2):
        if vis[i]==-1:
            q=deque()
            q.append(i)
            while len(q)!=0:
                x=q.popleft()
                vis[x]=1
                for j in range(1,len(graph[x])):
                    if vis[graph[x][j]]==-1:
                        print(x,graph[x][j])
                        q.append(graph[x][j])

