Problem Statement

You are given a string s consisting of two kinds of characters, 0 and 1. Print the string obtained by replacing 0 with 1 and 1 with 0 in s.

Constraints

• The length of s is between 1 and 10, inclusive.
• s consists of two kinds of characters, 0 and 1.

Sample Input 1

01

Sample Output 1

10

The 1-st character of s is 1, so the 1-st character to print is 0. The 2-nd character of s is 0, so the 2-nd character to print is 1.

Sample Input 2

1011

Sample Output 2

0100

Sample Input 3

100100001

Sample Output 3

011011110

Problem Statement

Given a string S, print AC if it perfectly matches Hello,World!; otherwise, print WA.

Constraints

• 1 \le |S| \le 15
• S consists of English lowercase letters, English uppercase letters, ,, and !.

Sample Input 1

Hello,World!

Sample Output 1

AC

The string S perfectly matches Hello,World!.

Sample Input 2

Hello,world!

Sample Output 2

WA

The seventh character from the beginning should be an uppercase W in Hello,World!, but S has a lowercase w in that position. Thus, S does not match Hello,World!.

Sample Input 3

Hello!World!

Sample Output 3

WA

Problem Statement

You are given a sequence A=(A_0,A_1,\dots,A_{63}) of length 64 consisting of 0 and 1.

Find A_0 2^0 + A_1 2^1 + \dots + A_{63} 2^{63}.

Constraints

• A_i is 0 or 1.

Sample Input 1

1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Sample Output 1

13

A_0 2^0 + A_1 2^1 + \dots + A_{63} 2^{63} = 2^0 + 2^2 + 2^3 = 13.

Sample Input 2

1 0 1 0 1 0 0 0 0 1 0 0 1 1 0 1 1 1 1 0 0 0 1 0 0 1 1 1 1 1 1 0 0 0 0 1 0 1 0 1 0 1 1 1 1 0 0 1 1 0 0 0 0 1 0 1 0 1 0 1 0 0 0 0

Sample Output 2

766067858140017173

Problem Statement

You are given a horizontally written text. Convert it to vertical writing, filling spaces with *.

You are given N strings S_1, S_2, \dots, S_N consisting of lowercase English letters. Let M be the maximum length of these strings.

Print M strings T_1, T_2, \dots, T_M that satisfy the following conditions:

• Each T_i consists of lowercase English letters and *.
• Each T_i does not end with *.
• For each 1 \leq i \leq N, the following holds:
  • For each 1 \leq j \leq |S_i|, the (N-i+1)-th character of T_j exists, and the concatenation of the (N-i+1)-th characters of T_1, T_2, \dots, T_{|S_i|} in this order equals S_i.
  • For each |S_i| + 1 \leq j \leq M, the (N-i+1)-th character of T_j either does not exist or is *.

Here, |S_i| denotes the length of the string S_i.

Constraints

• N is an integer between 1 and 100, inclusive.
• Each S_i is a string of lowercase English letters with length between 1 and 100, inclusive.

Sample Input 1

3
abc
de
fghi

Sample Output 1

fda
geb
h*c
i

Placing * as the 2nd character of T_3 puts the c in the correct position. On the other hand, placing * as the 2nd and 3rd characters of T_4 would make T_4 end with *, which violates the condition.

Sample Input 2

3
atcoder
beginner
contest

Sample Output 2

cba
oet
ngc
tio
end
sne
ter
*r

Problem Statement

Poem Online Judge (POJ) is an online judge that gives scores to submitted strings.
There were N submissions to POJ. In the i-th earliest submission, string S_i was submitted, and a score of T_i was given. (The same string may have been submitted multiple times.)
Note that POJ may not necessarily give the same score to submissions with the same string.

A submission is said to be an original submission if the string in the submission is never submitted in any earlier submission.
A submission is said to be the best submission if it is an original submission with the highest score. If there are multiple such submissions, only the earliest one is considered the best submission.

Find the index of the best submission.

Constraints

• 1 \leq N \leq 10^5
• S_i is a string consisting of lowercase English characters.
• S_i has a length between 1 and 10, inclusive.
• 0 \leq T_i \leq 10^9
• N and T_i are integers.

Sample Input 1

3
aaa 10
bbb 20
aaa 30

Sample Output 1

2

We will refer to the i-th earliest submission as Submission i.
Original submissions are Submissions 1 and 2. Submission 3 is not original because it has the same string as that in Submission 1.
Among the original submissions, Submission 2 has the highest score. Therefore, this is the best submission.

Sample Input 2

5
aaa 9
bbb 10
ccc 10
ddd 10
bbb 11

Sample Output 2

2

Original submissions are Submissions 1, 2, 3, and 4.
Among them, Submissions 2, 3, and 4 have the highest scores. In this case, the earliest submission among them, Submission 2, is the best.
As in this sample, beware that if multiple original submissions have the highest scores, only the one with the earliest among them is considered the best submission.

Sample Input 3

10
bb 3
ba 1
aa 4
bb 1
ba 5
aa 9
aa 2
ab 6
bb 5
ab 3

Sample Output 3

8

Problem Statement

We have a sequence of N numbers: A = (a_1, a_2, \dots, a_N).
Process the Q queries explained below.

• Query i: You are given a pair of integers (x_i, k_i). Let us look at the elements of A one by one from the beginning: a_1, a_2, \dots Which element will be the k_i-th occurrence of the number x_i?
  Print the index of that element, or -1 if there is no such element.

Constraints

• 1 \leq N \leq 2 \times 10^5
• 1 \leq Q \leq 2 \times 10^5
• 0 \leq a_i \leq 10^9 (1 \leq i \leq N)
• 0 \leq x_i \leq 10^9 (1 \leq i \leq Q)
• 1 \leq k_i \leq N (1 \leq i \leq Q)
• All values in input are integers.

Sample Input 1

6 8
1 1 2 3 1 2
1 1
1 2
1 3
1 4
2 1
2 2
2 3
4 1

Sample Output 1

1
2
5
-1
3
6
-1
-1

1 occurs in A at a_1, a_2, a_5. Thus, the answers to Query 1 through 4 are 1, 2, 5, -1 in this order.

Sample Input 2

3 2
0 1000000000 999999999
1000000000 1
123456789 1

Sample Output 2

2
-1

Problem Statement

There is a grid with N rows and N columns, where N is an odd number at most 45.

Let (i,j) denote the cell at the i-th row from the top and j-th column from the left.

In this grid, you will place Takahashi and a dragon consisting of N^2-1 parts numbered 1 to N^2-1 in such a way that satisfies the following conditions:

• Takahashi must be placed at the center of the grid, that is, in cell (\frac{N+1}{2},\frac{N+1}{2}).
• Except for the cell where Takahashi is, exactly one dragon part must be placed in each cell.
• For every integer x satisfying 2 \leq x \leq N^2-1, the dragon part x must be placed in a cell adjacent by an edge to the cell containing part x-1.
  • Cells (i,j) and (k,l) are said to be adjacent by an edge if and only if |i-k|+|j-l|=1.

Print one way to arrange the parts to satisfy the conditions. It is guaranteed that there is at least one arrangement that satisfies the conditions.

Constraints

• 3 \leq N \leq 45
• N is odd.

Sample Input 1

5

Sample Output 1

1 2 3 4 5
16 17 18 19 6
15 24 T 20 7
14 23 22 21 8
13 12 11 10 9

The following output also satisfies all the conditions and is correct.

9 10 11 14 15
8 7 12 13 16
5 6 T 18 17
4 3 24 19 20 
1 2 23 22 21

On the other hand, the following outputs are incorrect for the reasons given.

Takahashi is not at the center.

1 2 3 4 5
10 9 8 7 6
11 12 13 14 15
20 19 18 17 16
21 22 23 24 T

The cells containing parts 23 and 24 are not adjacent by an edge.

1 2 3 4 5
10 9 8 7 6
11 12 24 22 23
14 13 T 21 20
15 16 17 18 19

Problem Statement

You are given integers N and M. Find the remainder when \lfloor N/M \rfloor is divided by \color{red}{10007}.
Here, \lfloor x \rfloor denotes the largest integer not exceeding x. For example, \lfloor 3.14 \rfloor=3 and \lfloor 10 \rfloor = 10.

In this problem, N is not given directly; instead, it is given in run-length encoded form.
Specifically, N is represented by a sequence of K pairs of a digit c_i and an integer l_i.
To recover the original N, use the following procedure.

• Initially, let string S be the empty string.
• For i=1,2,\dots,K, repeat the following.
  • Append l_i copies of digit c_i to the end of S.
• Interpret the final S as a single integer; that integer is N.

Constraints

• 1 \le M \le 10^4
• 1 \le K \le 10^5
• c_i is one of the digits 0,1,2,3,4,5,6,7,8,9.
• 1 \le l_i \le 10^9
• c_1 \neq 0
• M,K,l_i are integers.

Sample Input 1

6 7
3 1
1 1
6 1
2 2
7 2
6 2

Sample Output 1

3797

In this input, N=316227766 and M=7.
\lfloor 316227766/7 \rfloor = 45175395, and the remainder when this is divided by 10007 is 3797, which is the final answer.

Sample Input 2

1 1
1 1

Sample Output 2

1

Sample Input 3

10 9999
9 419921892
9 923650333
6 476449815
1 8837775
2 141135534
5 462618481
3 202652735
0 771538044
4 321458589
0 570032864

Sample Output 3

8437

Problem Statement

You are given positive integers N, M, K, and a sequence of positive integers of length N, (C_1, C_2, \ldots, C_N). For each r = 0, 1, 2, \ldots, N-1, print the answer to the following problem.

There is a sequence of N colored balls. For i = 1, 2, \ldots, N, the color of the i-th ball from the beginning of the sequence is C_i. Additionally, there are M empty boxes numbered 1 to M.

Determine the total number of balls in the boxes after performing the following steps.

• First, perform the following operation r times.

  • Move the frontmost ball in the sequence to the end of the sequence.

• Then, repeat the following operation as long as at least one ball remains in the sequence.

  • If there is a box that already contains at least one but fewer than K balls of the same color as the frontmost ball in the sequence, put the frontmost ball into that box.
  • If there is no such box,
    • If there is an empty box, put the frontmost ball into the one with the smallest box number.
    • If there are no empty boxes, eat the frontmost ball without putting it into any box.

Constraints

• All input values are integers.
• 1 \leq N \leq 2 \times 10^5
• 1 \leq M, K \leq N
• 1 \leq C_i \leq N

Sample Input 1

7 2 2
1 2 3 5 2 5 4

Sample Output 1

3
3
3
4
4
3
2

For example, let us explain the procedure for r = 1. First, perform the operation "Move the frontmost ball in the sequence to the end of the sequence" once, and the sequence of ball colors becomes (2, 3, 5, 2, 5, 4, 1). Then, proceed with the operation of putting balls into boxes as follows:

• First operation: The color of the frontmost ball is 2. There is no box with at least one but fewer than two balls of color 2, so put the frontmost ball into the empty box with the smallest box number, box 1.
• Second operation: The color of the frontmost ball is 3. There is no box with at least one but fewer than two balls of color 3, so put the frontmost ball into the empty box with the smallest box number, box 2.
• Third operation: The color of the frontmost ball is 5. There is no box with at least one but fewer than two balls of color 5 and no empty boxes, so eat the frontmost ball.
• Fourth operation: The color of the frontmost ball is 2. There is a box, box 1, with at least one but fewer than two balls of color 2, so put the frontmost ball into box 1.
• Fifth operation: The color of the frontmost ball is 5. There is no box with at least one but fewer than two balls of color 5 and no empty boxes, so eat the frontmost ball.
• Sixth operation: The color of the frontmost ball is 4. There is no box with at least one but fewer than two balls of color 4 and no empty boxes, so eat the frontmost ball.
• Seventh operation: The color of the frontmost ball is 1. There is no box with at least one but fewer than two balls of color 1 and no empty boxes, so eat the frontmost ball.

The final total number of balls in the boxes is 3, so the answer to the problem for r = 1 is 3.

Sample Input 2

20 5 4
20 2 20 2 7 3 11 20 3 8 7 9 1 11 8 20 2 18 11 18

Sample Output 2

14
14
14
14
13
13
13
11
8
9
9
11
13
14
14
14
14
14
14
13