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## 문제

You are given N intervals. An interval can be represented by two positive integers Li and Ri - the interval starts at Li and ends at Ri, represented as [Li,Ri]. Intervals may not be unique, so there might be multiple intervals with both equal Li and equal Ri.

You are allowed to perform a maximum of C cuts. A cut at X will cut all intervals [L,R] for which L<X and X<R. Cutting an interval at X is defined as splitting the interval into two intervals - [L,X] and [X,R]. Note that cuts can only be performed at integer points. Also, cutting at an endpoint of an interval (X=L or X=R) has no effect and does not split the interval.

You need to find the maximum number of intervals that can be obtained through a maximum of C cuts.

## 입력

The first line of the input contains the number of test cases, T. T test cases follow.

Each test case starts with a line containing two integers, N and C, denoting the number of intervals and the maximum number of cuts you can perform respectively. N lines follow.

The i-th line contains two integers Li and Ri, describing the i-th interval.

## 출력

For each test case, output one line containing Case #x: y, where x is the test case number (starting from 1) and y is the maximum number of intervals that can be obtained through at most C cuts, as described above.

• 1 ≤ T ≤ 100.

## Test Set 1 (9점)

시간 제한: 20 초

• 1 ≤ N ≤ 500.
• 1 ≤ C ≤ 105.
• 1 ≤ Li < Ri ≤ 104 for all i.

## Test Set 2 (12점)

시간 제한: 40 초

• 1 ≤ N ≤ 105.
• 1 ≤ C ≤ 1018.
• 1 ≤ Li < Ri ≤ 1013 for all i.

## 예제 입력 1

1
3 3
1 3
2 4
1 4


## 예제 출력 1

Case #1: 7


## 힌트

In the provided sample, cuts should be performed at 2 and 3 to get the maximum number of intervals.

After the first cut at 2, the intervals would be {[1,2],[2,3],[2,4],[1,2],[2,4]}.

After the second cut at 3, the intervals would be {[1,2],[2,3],[2,3],[3,4],[1,2],[2,3],[3,4]}.

It can be seen that no interval can be cut further, so the answer is 7.

## 채점 및 기타 정보

• 예제는 채점하지 않는다.