Problem Statement

Given is a lowercase English letter C that is not z. Print the letter that follows C in alphabetical order.

Constraints

• C is a lowercase English letter that is not z.

Sample Input 1

a

Sample Output 1

b

a is followed by b.

Sample Input 2

y

Sample Output 2

z

y is followed by z.

Problem Statement

Takahashi is taking exams on N subjects. The score on each subject will be an integer between 0 and K (inclusive).

He has already taken exams on N-1 subjects and scored A_i points on the i-th subject.

His goal is to achieve the average score of M points or above on the N subjects.

Print the minimum number of points Takahashi needs on the final subject to achieve his goal.

If the goal is unachievable, print -1 instead.

Constraints

• 2 \leq N \leq 100
• 1 \leq K \leq 100
• 1 \leq M \leq K
• 0 \leq A_i \leq K
• All values in input are integers.

Sample Input 1

5 10 7
8 10 3 6

Sample Output 1

8

If he scores 8 points on the final subject, his average score will be (8+10+3+6+8)/5 = 7 points, which meets the goal.

Sample Input 2

4 100 60
100 100 100

Sample Output 2

0

Scoring 0 points on the final subject still meets the goal.

Sample Input 3

4 100 60
0 0 0

Sample Output 3

-1

He can no longer meet the goal.

Problem Statement

Takahashi participated in a contest on AtCoder.

The contest had N problems.

Takahashi made M submissions during the contest.

The i-th submission was made for the p_i-th problem and received the verdict S_i (AC or WA).

The number of Takahashi's correct answers is the number of problems on which he received an AC once or more.

The number of Takahashi's penalties is the sum of the following count for the problems on which he received an AC once or more: the number of WAs received before receiving an AC for the first time on that problem.

Find the numbers of Takahashi's correct answers and penalties.

Constraints

• N, M, and p_i are integers.
• 1 \leq N \leq 10^5
• 0 \leq M \leq 10^5
• 1 \leq p_i \leq N
• S_i is AC or WA.

Sample Input 1

2 5
1 WA
1 AC
2 WA
2 AC
2 WA

Sample Output 1

2 2

In his second submission, he received an AC on the first problem for the first time. Before this, he received one WA on this problem.

In his fourth submission, he received an AC on the second problem for the first time. Before this, he received one WA on this problem.

Thus, he has two correct answers and two penalties.

Sample Input 2

100000 3
7777 AC
7777 AC
7777 AC

Sample Output 2

1 0

Note that it is pointless to get an AC more than once on the same problem.

Sample Input 3

6 0

Sample Output 3

0 0

Problem Statement

Takahashi has a maze, which is a grid of H \times W squares with H horizontal rows and W vertical columns.

The square at the i-th row from the top and the j-th column is a "wall" square if S_{ij} is #, and a "road" square if S_{ij} is ..

From a road square, you can move to a horizontally or vertically adjacent road square.

You cannot move out of the maze, move to a wall square, or move diagonally.

Takahashi will choose a starting square and a goal square, which can be any road squares, and give the maze to Aoki.

Aoki will then travel from the starting square to the goal square, in the minimum number of moves required.

In this situation, find the maximum possible number of moves Aoki has to make.

Constraints

• 1 \leq H,W \leq 20
• S_{ij} is . or #.
• S contains at least two occurrences of ..
• Any road square can be reached from any road square in zero or more moves.

Sample Input 1

3 3
...
...
...

Sample Output 1

4

If Takahashi chooses the top-left square as the starting square and the bottom-right square as the goal square, Aoki has to make four moves.

Sample Input 2

3 5
...#.
.#.#.
.#...

Sample Output 2

10

If Takahashi chooses the bottom-left square as the starting square and the top-right square as the goal square, Aoki has to make ten moves.

Problem Statement

For a finite set of integers X, let f(X)=\max X - \min X.

Given are N integers A_1,...,A_N.

We will choose K of them and let S be the set of the integers chosen. If we distinguish elements with different indices even when their values are the same, there are {}_N C_K ways to make this choice. Find the sum of f(S) over all those ways.

Since the answer can be enormous, print it \bmod (10^9+7).

Constraints

• 1 \leq N \leq 10^5
• 1 \leq K \leq N
• |A_i| \leq 10^9

Sample Input 1

4 2
1 1 3 4

Sample Output 1

11

There are six ways to choose S: \{1,1\},\{1,3\},\{1,4\},\{1,3\},\{1,4\}, \{3,4\} (we distinguish the two 1s). The value of f(S) for these choices are 0,2,3,2,3,1, respectively, for the total of 11.

Sample Input 2

6 3
10 10 10 -10 -10 -10

Sample Output 2

360

There are 20 ways to choose S. In 18 of them, f(S)=20, and in 2 of them, f(S)=0.

Sample Input 3

3 1
1 1 1

Sample Output 3

0

Sample Input 4

10 6
1000000000 1000000000 1000000000 1000000000 1000000000 0 0 0 0 0

Sample Output 4

999998537

Print the sum \bmod (10^9+7).

Problem Statement

Given are N points (x_i, y_i) in a two-dimensional plane.

Find the minimum radius of a circle such that all the points are inside or on it.

Constraints

• 2 \leq N \leq 50
• 0 \leq x_i \leq 1000
• 0 \leq y_i \leq 1000
• The given N points are all different.
• The values in input are all integers.

Sample Input 1

2
0 0
1 0

Sample Output 1

0.500000000000000000

Both points are contained in the circle centered at (0.5,0) with a radius of 0.5.

Sample Input 2

3
0 0
0 1
1 0

Sample Output 2

0.707106781186497524

Sample Input 3

10
10 9
5 9
2 0
0 0
2 7
3 3
2 5
10 0
3 7
1 9

Sample Output 3

6.726812023536805158

If the absolute or relative error from our answer is at most 10^{-6}, the output will be considered correct.