Problem Statement

You are given a string S consisting of lowercase English characters. The length of S is between 1 and 3, inclusive.

Print the string of length 6 that is a repetition of S.

It can be shown that there uniquely exists such a string under the Constraints of this problem.

Constraints

• S is a string consisting of lowercase English characters of length between 1 and 3, inclusive.

Sample Input 1

abc

Sample Output 1

abcabc

These are strings that are repetitions of S = abc: abc, abcabc, abcabcabc, abcabcabcabc, and so on. Among them, abcabc has the length of 6, so abcabc should be printed.

Sample Input 2

zz

Sample Output 2

zzzzzz

Problem Statement

Given N, print 2^N.

Constraints

• 0 \leq N \leq 30
• N is an integer.

Sample Input 1

3

Sample Output 1

8

We have 2^3=8.

Sample Input 2

30

Sample Output 2

1073741824

Problem Statement

You are given an integer sequence A=(A_1,\ldots,A_N) of length N. Here, A_1, A_2, \ldots, A_N are all distinct.

Which element in A is the second largest?

Constraints

• 2 \leq N \leq 100
• 1 \leq A_i \leq 10^9
• A_1, A_2, \ldots, A_N are all distinct.
• All input values are integers.

Sample Input 1

4
8 2 5 1

Sample Output 1

3

The second largest element in A is A_3, so print 3.

Sample Input 2

8
1 2 3 4 5 10 9 11

Sample Output 2

6

Problem Statement

There are N people numbered 1, 2, \dots, N in the xy-plane. Person i is at the coordinates (X_i, Y_i).
K of these people, Persons A_1, A_2, \dots, A_K, will receive lights of the same strength.
When a person at coordinates (x, y) has a light of strength R, it lights up the interior of a circle of radius R centered at (x, y) (including the boundary).
Find the minimum strength of the lights needed for every person to be lit by at least one light.

Constraints

• All values in input are integers.
• 1 \le K < N \le 1000
• 1 \le A_1 < A_2 < \dots < A_K \le N
• |X_i|,|Y_i| \le 10^5
• (X_i,Y_i) \neq (X_j,Y_j), if i \neq j.

Sample Input 1

4 2
2 3
0 0
0 1
1 2
2 0

Sample Output 1

2.23606797749978969

This input contains four people. Among them, Persons 2 and 3 will have lights.
Every person will be lit by at least one light if R \ge \sqrt{5} \approx 2.236068.

Sample Input 2

2 1
2
-100000 -100000
100000 100000

Sample Output 2

282842.712474619009

Sample Input 3

8 3
2 6 8
-17683 17993
93038 47074
58079 -57520
-41515 -89802
-72739 68805
24324 -73073
71049 72103
47863 19268

Sample Output 3

130379.280458974768

Problem Statement

There is a 3\times3 grid with numbers between 1 and 9, inclusive, written in each square. The square at the i-th row from the top and j-th column from the left (1\leq i\leq3,1\leq j\leq3) contains the number c _ {i,j}.

The same number may be written in different squares, but not in three consecutive cells vertically, horizontally, or diagonally. More precisely, it is guaranteed that c _ {i,j} satisfies all of the following conditions.

• c _ {i,1}=c _ {i,2}=c _ {i,3} does not hold for any 1\leq i\leq3.
• c _ {1,j}=c _ {2,j}=c _ {3,j} does not hold for any 1\leq j\leq3.
• c _ {1,1}=c _ {2,2}=c _ {3,3} does not hold.
• c _ {3,1}=c _ {2,2}=c _ {1,3} does not hold.

Takahashi will see the numbers written in each cell in random order. He will get disappointed when there is a line (vertical, horizontal, or diagonal) that satisfies the following condition.

• The first two squares he sees contain the same number, but the last square contains a different number.

Find the probability that Takahashi sees the numbers in all the squares without getting disappointed.

Constraints

• c _ {i,j}\in\lbrace1,2,3,4,5,6,7,8,9\rbrace\ (1\leq i\leq3,1\leq j\leq3)
• c _ {i,1}=c _ {i,2}=c _ {i,3} does not hold for any 1\leq i\leq3.
• c _ {1,j}=c _ {2,j}=c _ {3,j} does not hold for any 1\leq j\leq3.
• c _ {1,1}=c _ {2,2}=c _ {3,3} does not hold.
• c _ {3,1}=c _ {2,2}=c _ {1,3} does not hold.

Sample Input 1

3 1 9
2 5 6
2 7 1

Sample Output 1

0.666666666666666666666666666667

For example, if Takahashi sees c _ {3,1}=2,c _ {2,1}=2,c _ {1,1}=3 in this order, he will get disappointed.

On the other hand, if Takahashi sees c _ {1,1},c _ {1,2},c _ {1,3},c _ {2,1},c _ {2,2},c _ {2,3},c _ {3,1},c _ {3,2},c _ {3,3} in this order, he will see all numbers without getting disappointed.

The probability that Takahashi sees all the numbers without getting disappointed is \dfrac 23. Your answer will be considered correct if the absolute error from the true value is at most 10 ^ {-8}, so outputs such as 0.666666657 and 0.666666676 would also be accepted.

Sample Input 2

7 7 6
8 6 8
7 7 6

Sample Output 2

0.004982363315696649029982363316

Sample Input 3

3 6 7
1 9 7
5 7 5

Sample Output 3

0.4

Problem Statement

A non-negative integer n is called a good integer when it satisfies the following condition:

• All digits in the decimal notation of n are even numbers (0, 2, 4, 6, and 8).

For example, 0, 68, and 2024 are good integers.

You are given an integer N. Find the N-th smallest good integer.

Constraints

• 1 \leq N \leq 10^{12}
• N is an integer.

Sample Input 1

8

Sample Output 1

24

The good integers in ascending order are 0, 2, 4, 6, 8, 20, 22, 24, 26, 28, \dots.
The eighth smallest is 24, which should be printed.

Sample Input 2

133

Sample Output 2

2024

Sample Input 3

31415926535

Sample Output 3

2006628868244228

Problem Statement

There is a deck consisting of N face-down cards with an integer from 1 through N written on them. The integer on the i-th card from the top is P_i.

Using this deck, you will perform N moves, each consisting of the following steps:

• Draw the topmost card from the deck. Let X be the integer written on it.
• Stack the drawn card, face up, onto the card with the smallest integer among the face-up topmost cards on the table with an integer greater than or equal to X written on them. If there is no such card on the table, put the drawn card on the table, face up, without stacking it onto any card.
• Then, if there is a pile consisting of K face-up cards on the table, eat all those cards. The eaten cards all disappear from the table.

For each card, find which of the N moves eats it. If the card is not eaten until the end, report that fact.

Constraints

• All values in input are integers.
• 1 \le K \le N \le 2 \times 10^5
• P is a permutation of (1,2,\dots,N) (i.e. a sequence obtained by rearranging (1,2,\dots,N)).

Sample Input 1

5 2
3 5 2 1 4

Sample Output 1

4
3
3
-1
4

In this input, P=(3,5,2,1,4) and K=2.

• In the 1-st move, the card with 3 written on it is put on the table, face up, without stacked onto any card.
• In the 2-nd move, the card with 5 written on it is put on the table, face up, without stacked onto any card.
• In the 3-rd move, the card with 2 written on it is stacked, face up, onto the card with 3 written on it.
  • Now there is a pile consisting of K=2 face-up cards, on which 2 and 3 from the top are written, so these cards are eaten.
• In the 4-th move, the card with 1 written on it is stacked, face up, onto the card with 5 written on it.
  • Now there is a pile consisting of K=2 face-up cards, on which 1 and 5 from the top are written, so these cards are eaten.
• In the 5-th move, the card with 4 written on it is put on the table, face up, without stacked onto any card.
• The card with 4 written on it was not eaten until the end.

Sample Input 2

5 1
1 2 3 4 5

Sample Output 2

1
2
3
4
5

If K=1, every card is eaten immediately after put on the table within a single move.

Sample Input 3

15 3
3 14 15 9 2 6 5 13 1 7 10 11 8 12 4

Sample Output 3

9
9
9
15
15
6
-1
-1
6
-1
-1
-1
-1
6
15

Problem Statement

Let us call a positive integer n that satisfies the following condition an arithmetic number.

• Let d_i be the i-th digit of n from the top (when n is written in base 10 without unnecessary leading zeros.) Then, (d_2-d_1)=(d_3-d_2)=\dots=(d_k-d_{k-1}) holds, where k is the number of digits in n.
  • This condition can be rephrased into the sequence (d_1,d_2,\dots,d_k) being arithmetic.
  • If n is a 1-digit integer, it is assumed to be an arithmetic number.

For example, 234,369,86420,17,95,8,11,777 are arithmetic numbers, while 751,919,2022,246810,2356 are not.

Find the smallest arithmetic number not less than X.

Constraints

• X is an integer between 1 and 10^{17} (inclusive).

Sample Input 1

152

Sample Output 1

159

The smallest arithmetic number not less than 152 is 159.

Sample Input 2

88

Sample Output 2

88

X itself may be an arithmetic number.

Sample Input 3

8989898989

Sample Output 3

9876543210

Problem Statement

Find one shortest palindrome that has S as its prefix.

Constraints

• S is a string of length between 1 and 500000, inclusive, consisting of uppercase English letters.

Sample Input 1

ABC

Sample Output 1

ABCBA

ABCBA is a shortest palindrome that has S= ABC as its prefix.

Sample Input 2

Z

Sample Output 2

Z

Z is a shortest palindrome that has S= Z as its prefix.

Sample Input 3

TREE

Sample Output 3

TREERT

TREERT is a shortest palindrome that has S= TREE as its prefix.