Colors and Intervals
题意翻译
$n \times k$ 个格子,编号从 $1$ 到 $n \times k$,染成 $n$ 种颜色,每种颜色恰好 $k$ 个。
构造 $n$ 个区间,第 $i$ 个区间 $[a_i, b_i]$ 满足
- $1 \le a_i < b_i \le n \times k$
- 第 $a_i$ 个和第 $b_i$ 个格子的颜色都是 $i$。
- 每个格子被包含不超过 $\lceil \frac{n}{k-1} \rceil$ 次。
题目描述
The numbers $ 1, \, 2, \, \dots, \, n \cdot k $ are colored with $ n $ colors. These colors are indexed by $ 1, \, 2, \, \dots, \, n $ . For each $ 1 \le i \le n $ , there are exactly $ k $ numbers colored with color $ i $ .
Let $ [a, \, b] $ denote the interval of integers between $ a $ and $ b $ inclusive, that is, the set $ \{a, \, a + 1, \, \dots, \, b\} $ . You must choose $ n $ intervals $ [a_1, \, b_1], \, [a_2, \, b_2], \, \dots, [a_n, \, b_n] $ such that:
- for each $ 1 \le i \le n $ , it holds $ 1 \le a_i < b_i \le n \cdot k $ ;
- for each $ 1 \le i \le n $ , the numbers $ a_i $ and $ b_i $ are colored with color $ i $ ;
- each number $ 1 \le x \le n \cdot k $ belongs to at most $ \left\lceil \frac{n}{k - 1} \right\rceil $ intervals.
One can show that such a family of intervals always exists under the given constraints.
输入输出格式
输入格式
The first line contains two integers $ n $ and $ k $ ( $ 1 \le n \le 100 $ , $ 2 \le k \le 100 $ ) — the number of colors and the number of occurrences of each color.
The second line contains $ n \cdot k $ integers $ c_1, \, c_2, \, \dots, \, c_{nk} $ ( $ 1 \le c_j \le n $ ), where $ c_j $ is the color of number $ j $ . It is guaranteed that, for each $ 1 \le i \le n $ , it holds $ c_j = i $ for exactly $ k $ distinct indices $ j $ .
输出格式
Output $ n $ lines. The $ i $ -th line should contain the two integers $ a_i $ and $ b_i $ .
If there are multiple valid choices of the intervals, output any.
输入输出样例
输入样例 #1
4 3
2 4 3 1 1 4 2 3 2 1 3 4
输出样例 #1
4 5
1 7
8 11
6 12
输入样例 #2
1 2
1 1
输出样例 #2
1 2
输入样例 #3
3 3
3 1 2 3 2 1 2 1 3
输出样例 #3
6 8
3 7
1 4
输入样例 #4
2 3
2 1 1 1 2 2
输出样例 #4
2 3
5 6
说明
In the first sample, each number can be contained in at most $ \left\lceil \frac{4}{3 - 1} \right\rceil = 2 $ intervals. The output is described by the following picture:
![](https://cdn.luogu.com.cn/upload/vjudge_pic/CF1552E/357ee458ed0b41175ab4d6d5282731204fd88de0.png)In the second sample, the only interval to be chosen is forced to be $ [1, \, 2] $ , and each number is indeed contained in at most $ \left\lceil \frac{1}{2 - 1} \right\rceil = 1 $ interval.
In the third sample, each number can be contained in at most $ \left\lceil \frac{3}{3 - 1} \right\rceil = 2 $ intervals. The output is described by the following picture:
![](https://cdn.luogu.com.cn/upload/vjudge_pic/CF1552E/5bede56472d45bf512432afa3ad4f14a8a3b2bc1.png)