Problem Statement

In an xy-coordinate plane whose x-axis is oriented to the right and whose y-axis is oriented upwards, rotate a point (a, b) around the origin d degrees counterclockwise and find the new coordinates of the point.

Constraints

• -1000 \leq a,b \leq 1000
• 1 \leq d \leq 360
• All values in input are integers.

Sample Input 1

2 2 180

Sample Output 1

-2 -2

When (2, 2) is rotated around the origin 180 degrees counterclockwise, it becomes the symmetric point of (2, 2) with respect to the origin, which is (-2, -2).

Sample Input 2

5 0 120

Sample Output 2

-2.49999999999999911182 4.33012701892219364908

When (5, 0) is rotated around the origin 120 degrees counterclockwise, it becomes (-\frac {5}{2} , \frac {5\sqrt{3}}{2}).
This sample output does not precisely match these values, but the errors are small enough to be considered correct.

Sample Input 3

0 0 11

Sample Output 3

0.00000000000000000000 0.00000000000000000000

Since (a, b) is the origin (the center of rotation), a rotation does not change its coordinates.

Sample Input 4

15 5 360

Sample Output 4

15.00000000000000177636 4.99999999999999555911

A 360-degree rotation does not change the coordinates of a point.

Sample Input 5

-505 191 278

Sample Output 5

118.85878514480690171240 526.66743699786547949770

Problem Statement

Takahashi has N foods in his house. The i-th food has the tastiness of A_i.
He dislikes K of these foods: for each i=1,2,\ldots,K, he dislikes the B_i-th food.

Out of the foods with the greatest tastiness among the N foods, Takahashi will randomly choose one and eat it.
If he has a chance to eat something he dislikes, print Yes; otherwise, print No.

Constraints

• 1\leq K\leq N\leq 100
• 1\leq A_i\leq 100
• 1\leq B_i\leq N
• All B_i are distinct.
• All values in input are integers.

Sample Input 1

5 3
6 8 10 7 10
2 3 4

Sample Output 1

Yes

Among the five foods, the ones with the greatest tastiness are Food 3 and 5, of which he eats one.
He dislikes Food 2, 3, and 4, one of which he has a chance to eat: Food 3.
Therefore, the answer is Yes.

Sample Input 2

5 2
100 100 100 1 1
5 4

Sample Output 2

No

The foods with the greatest tastiness are Food 1, 2, and 3, none of which he has a chance to eat.

Sample Input 3

2 1
100 1
2

Sample Output 3

No

The food with the greatest tastiness is Food 1, which he has no chance to eat.

Problem Statement

This problem is a sub-problem of Problem F (Operate K), with K=1.
You can solve this problem by submitting a correct solution for Problem F to this problem.

Determine whether it is possible to perform the following operation on string S between 0 and K times, inclusive, to make it identical to string T.

• Choose one of the following three operations and execute it.
  • Insert any one character at any position in S (possibly the beginning or end).
  • Delete one character from S.
  • Choose one character in S and replace it with another character.

Constraints

• Each of S and T is a string of length between 1 and 500000, inclusive, consisting of lowercase English letters.
• \color{red}{K=1}

Sample Input 1

1
abc
agc

Sample Output 1

Yes

Replacing the second character b of abc with g converts abc to agc in one operation.

Sample Input 2

1
abc
awtf

Sample Output 2

No

abc cannot be converted to awtf in one operation.

Sample Input 3

1
abc
ac

Sample Output 3

Yes

Deleting the second character b of abc converts abc to ac in one operation.

Sample Input 4

1
back
black

Sample Output 4

Yes

Inserting l between the first and second characters of back converts back to black in one operation.

Sample Input 5

1
same
same

Sample Output 5

Yes

It is also possible that S = T from the beginning.

Sample Input 6

1
leap
read

Sample Output 6

No

Problem Statement

Find the K-th lexicographically smallest string among the strings that are permutations of a string S.

Constraints

• 1 \le |S| \le 8
• S consists of lowercase English letters.
• There are at least K distinct strings that are permutations of S.

Sample Input 1

aab 2

Sample Output 1

aba

There are three permutations of a string aab: \{ aab, aba, baa \}. The 2-nd lexicographically smallest of them is aba.

Sample Input 2

baba 4

Sample Output 2

baab

Sample Input 3

ydxwacbz 40320

Sample Output 3

zyxwdcba

Problem Statement

There are N sports players.

Among them, there are M incompatible pairs. The i-th incompatible pair (1\leq i\leq M) is the A_i-th and B_i-th players.

You will divide the players into T teams. Every player must belong to exactly one team, and every team must have one or more players. Additionally, for each i=1,2,\ldots,M, the A_i-th and B_i-th players must not belong to the same team.

Find the number of ways to satisfy these conditions. Here, two divisions are considered different when there are two players who belong to the same team in one division and different teams in the other.

Constraints

• 1\leq T\leq N\leq10
• 0\leq M\leq\dfrac{N(N-1)}2
• 1\leq A _ i\lt B _ i\leq N\ (1\leq i\leq M)
• (A _ i,B _ i)\neq (A _ j,B _ j)\ (1\leq i\lt j\leq M)
• All input values are integers.

Sample Input 1

5 2 2
1 3
3 4

Sample Output 1

4

The following four divisions satisfy the conditions.

No other division satisfies them, so print 4.

Sample Input 2

5 1 2
1 3
3 4

Sample Output 2

0

There may be no division that satisfies the conditions.

Sample Input 3

6 4 0

Sample Output 3

65

There may be no incompatible pair.

Sample Input 4

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

Sample Output 4

8001