Problem Statement

There is a rectangle in the xy-plane. Each edge of this rectangle is parallel to the x- or y-axis, and its area is not zero.

Given the coordinates of three of the four vertices of this rectangle, (x_1, y_1), (x_2, y_2), and (x_3, y_3), find the coordinates of the other vertex.

Constraints

• -100 \leq x_i, y_i \leq 100
• There uniquely exists a rectangle with all of (x_1, y_1), (x_2, y_2), (x_3, y_3) as vertices, edges parallel to the x- or y-axis, and a non-zero area.
• All values in input are integers.

Sample Input 1

-1 -1
-1 2
3 2

Sample Output 1

3 -1

The other vertex of the rectangle with vertices (-1, -1), (-1, 2), (3, 2) is (3, -1).

Sample Input 2

-60 -40
-60 -80
-20 -80

Sample Output 2

-20 -40

Problem Statement

You are given a string S of length 3 consisting of uppercase English letters.

Determine whether it is possible to rearrange the characters in S to make it match the string ABC.

Constraints

• S is a string of length 3 consisting of uppercase English letters.

Sample Input 1

BAC

Sample Output 1

Yes

You can make S match ABC by swapping the first and second characters of S.

Sample Input 2

AAC

Sample Output 2

No

You cannot make S match ABC no matter how you rearrange the characters.

Sample Input 3

ABC

Sample Output 3

Yes

Sample Input 4

ARC

Sample Output 4

No

Problem Statement

Studying Kanbun, Takahashi is having trouble figuring out the order to read words. Help him out!

There are N integers from 1 through N arranged in a line in ascending order.
Between them are M "レ" marks. The i-th "レ" mark is between the integer a_i and integer (a_i + 1).

You read each of the N integers once by the following procedure.

• Consider an undirected graph G with N vertices numbered 1 through N and M edges. The i-th edge connects vertex a_i and vertex (a_i+1).
• Repeat the following operation until there is no unread integer:
  • let x be the minimum unread integer. Choose the connected component C containing vertex x, and read all the numbers of the vertices contained in C in descending order.

For example, suppose that integers and "レ" marks are arranged in the following order:

(In this case, N = 5, M = 3, and a = (1, 3, 4).)
Then, the order to read the integers is determined to be 2, 1, 5, 4, and 3, as follows:

• At first, the minimum unread integer is 1, and the connected component of G containing vertex 1 has vertices \lbrace 1, 2 \rbrace, so 2 and 1 are read in this order.
• Then, the minimum unread integer is 3, and the connected component of G containing vertex 3 has vertices \lbrace 3, 4, 5 \rbrace, so 5, 4, and 3 are read in this order.
• Now that all integers are read, terminate the procedure.

Given N, M, and (a_1, a_2, \dots, a_M), print the order to read the N integers.

Constraints

• 1 \leq N \leq 100
• 0 \leq M \leq N - 1
• 1 \leq a_1 \lt a_2 \lt \dots \lt a_M \leq N-1
• All values in the input are integers.

Sample Input 1

5 3
1 3 4

Sample Output 1

2 1 5 4 3

As described in the Problem Statement, if integers and "レ" marks are arranged in the following order:

then the integers are read in the following order: 2, 1, 5, 4, and 3.

Sample Input 2

5 0

Sample Output 2

1 2 3 4 5

There may be no "レ" mark.

Sample Input 3

10 6
1 2 3 7 8 9

Sample Output 3

4 3 2 1 5 6 10 9 8 7

Problem Statement

At the entrance of AtCoder Land, there is a single ticket booth where visitors line up to purchase tickets one by one. The purchasing process takes A seconds per person. Once the person at the front of the line finishes purchasing their ticket, the next person (if any) immediately starts their purchasing process.

Currently, there is no one in line at the ticket booth, and N people will come to buy tickets one after another. Specifically, the i-th person will arrive at the ticket booth T_i seconds from now. If there is already a line, they will join the end of it; if not, they will start the purchasing process immediately. Here, T_1 < T_2 < \dots < T_N.

For each i\ (1 \leq i \leq N), determine how many seconds from now the i-th person will finish purchasing their ticket.

Constraints

• 1 \leq N \leq 100
• 0 \leq T_1 < T_2 < \dots < T_N \leq 10^6
• 1 \leq A \leq 10^6
• All input values are integers.

Sample Input 1

3 4
0 2 10

Sample Output 1

4
8
14

The events proceed in the following order:

• At 0 seconds: The 1st person arrives at the ticket booth and starts the purchasing process.
• At 2 seconds: The 2nd person arrives at the ticket booth and joins the line behind the 1st person.
• At 4 seconds: The 1st person finishes purchasing their ticket, and the 2nd person starts the purchasing process.
• At 8 seconds: The 2nd person finishes purchasing their ticket.
• At 10 seconds: The 3rd person arrives at the ticket booth and starts the purchasing process.
• At 14 seconds: The 3rd person finishes purchasing their ticket.

Sample Input 2

3 3
1 4 7

Sample Output 2

4
7
10

The events proceed in the following order:

• At 1 second: The 1st person arrives at the ticket booth and starts the purchasing process.
• At 4 seconds: The 1st person finishes purchasing their ticket, and the 2nd person arrives at the ticket booth and starts the purchasing process.
• At 7 seconds: The 2nd person finishes purchasing their ticket, and the 3rd person arrives at the ticket booth and starts the purchasing process.
• At 10 seconds: The 3rd person finishes purchasing their ticket.

Sample Input 3

10 50000
120190 165111 196897 456895 540000 552614 561627 743796 757613 991216

Sample Output 3

170190
220190
270190
506895
590000
640000
690000
793796
843796
1041216

Problem Statement

Takahashi is going to read a manga series "Snuke-kun" in 10^9 volumes.
Initially, Takahashi has N books of this series. The i-th book is Volume a_i.

Takahashi may repeat the following operation any number of (possibly zero) times only before he begins to read:

• Do nothing if he has 1 or less books; otherwise, sell two of the books he has and buy one book of any volume instead.

Then, Takahashi reads Volume 1, Volume 2, Volume 3, \ldots, in order. However, when he does not have a book of the next volume to read, he stops reading the series (regardless of the other volumes he has).

Find the latest volume of the series that he can read up to. If he cannot read any, let the answer be 0.

Constraints

• 1 \leq N \leq 3 \times 10^5
• 1 \leq a_i \leq 10^9
• All values in the input are integers.

Sample Input 1

6
1 2 4 6 7 271

Sample Output 1

4

Before he begins to read the series, he may do the following operation: "sell books of Volumes 7 and 271 and buy one book of Volume 3 instead." Then, he has one book each of Volumes 1, 2, 3, 4, and 6.
If he then begins to read the series, he reads Volumes 1, 2, 3, and 4, then tries to read Volume 5. However, he does not have one, so he stops reading at this point.
Regardless of the choices in the operation, he cannot read Volume 5, so the answer is 4.

Sample Input 2

10
1 1 1 1 1 1 1 1 1 1

Sample Output 2

5

Takahashi may have multiple books of the same volume.
For this input, if he performs the following 4 operations before he begins to read the series, he can read up to Volume 5, which is the maximum:

• Sell two books of Volume 1 and buy a book of Volume 2 instead.
• Sell two books of Volume 1 and buy a book of Volume 3 instead.
• Sell two books of Volume 1 and buy a book of Volume 4 instead.
• Sell two books of Volume 1 and buy a book of Volume 5 instead.

Sample Input 3

1
5

Sample Output 3

0

Takahashi cannot read Volume 1.