CF1003E.Tree Constructing

普及/提高-

通过率：0%

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题目描述

The first line of the input contains three integers $n$ , $d$ and $k$ ( $1 \le n, d, k \le 4 \cdot 10^5$ ).

输入格式

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.

输出格式

无

输入输出样例

输入#1
```
6 3 3
```
输出#1
```
YES
3 1
4 1
1 2
5 2
2 6
```
输入#2
```
6 2 3
```
输出#2
```
NO
```

输入#3

10 4 3

输出#3

输入#4
```
8 5 3
```
输出#4
```
YES
2 5
7 2
3 7
3 1
1 6
8 7
4 3
```

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