Problem Statement

You are given a string S of length 16 consisting of 0 and 1.

If the i-th character of S is 0 for every even number i from 2 through 16, print Yes; otherwise, print No.

Constraints

• S is a string of length 16 consisting of 0 and 1.

Sample Input 1

1001000000001010

Sample Output 1

No

The 4-th character of S= 1001000000001010 is 1, so you should print No.

Sample Input 2

1010100000101000

Sample Output 2

Yes

Every even-positioned character in S= 1010100000101000 is 0, so you should print Yes.

Sample Input 3

1111111111111111

Sample Output 3

No

Every even-positioned character in S is 1. Particularly, they are not all 0, so you should print No.

Problem Statement

Print an arithmetic sequence with first term A, last term B, and common difference D.

You are only given inputs for which such an arithmetic sequence exists.

Constraints

• 1 \leq A \leq B \leq 100
• 1 \leq D \leq 100
• There is an arithmetic sequence with first term A, last term B, and common difference D.
• All input values are integers.

Sample Input 1

3 9 2

Sample Output 1

3 5 7 9

The arithmetic sequence with first term 3, last term 9, and common difference 2 is (3,5,7,9).

Sample Input 2

10 10 1

Sample Output 2

10

The arithmetic sequence with first term 10, last term 10, and common difference 1 is (10).

Problem Statement

N players with ID numbers 1, 2, \ldots, N are playing a card game.
Each player plays one card.

Each card has two parameters: color and rank, both of which are represented by positive integers.
For i = 1, 2, \ldots, N, the card played by player i has a color C_i and a rank R_i. All of R_1, R_2, \ldots, R_N are different.

Among the N players, one winner is decided as follows.

• If one or more cards with the color T are played, the player who has played the card with the greatest rank among those cards is the winner.
• If no card with the color T is played, the player who has played the card with the greatest rank among the cards with the color of the card played by player 1 is the winner. (Note that player 1 may win.)

Print the ID number of the winner.

Constraints

• 2 \leq N \leq 2 \times 10^5
• 1 \leq T \leq 10^9
• 1 \leq C_i \leq 10^9
• 1 \leq R_i \leq 10^9
• i \neq j \implies R_i \neq R_j
• All values in the input are integers.

Sample Input 1

4 2
1 2 1 2
6 3 4 5

Sample Output 1

4

Cards with the color 2 are played. Thus, the winner is player 4, who has played the card with the greatest rank, 5, among those cards.

Sample Input 2

4 2
1 3 1 4
6 3 4 5

Sample Output 2

1

No card with the color 2 is played. Thus, the winner is player 1, who has played the card with the greatest rank, 6, among the cards with the color of the card played by player 1 (color 1).

Sample Input 3

2 1000000000
1000000000 1
1 1000000000

Sample Output 3

1

Problem Statement

N AtCoder users have gathered to play AtCoder RPS 2. The i-th user's name is S_i and their rating is C_i.

AtCoder RPS 2 is played as follows:

• Assign the numbers 0, 1, \dots, N - 1 to the users in lexicographical order of their usernames.
• Let T be the sum of the ratings of the N users. The user assigned the number T \bmod N is the winner.

Print the winner's username.

Constraints

• 1 \leq N \leq 100
• S_i is a string consisting of lowercase English letters with length between 3 and 16, inclusive.
• S_1, S_2, \dots, S_N are all distinct.
• 1 \leq C_i \leq 4229
• C_i is an integer.

Sample Input 1

3
takahashi 2
aoki 6
snuke 5

Sample Output 1

snuke

The sum of the ratings of the three users is 13. Sorting their names in lexicographical order yields aoki, snuke, takahashi, so aoki is assigned number 0, snuke is 1, and takahashi is 2.

Since 13 \bmod 3 = 1, print snuke, who is assigned number 1.

Sample Input 2

3
takahashi 2813
takahashixx 1086
takahashix 4229

Sample Output 2

takahashix

Problem Statement

There is an N\times N grid with horizontal rows and vertical columns, where all squares are initially painted white. Let (i,j) denote the square at the i-th row and j-th column.

Takahashi has integers A and B, which are between 1 and N (inclusive). He will do the following operations.

• For every integer k such that \max(1-A,1-B)\leq k\leq \min(N-A,N-B), paint (A+k,B+k) black.
• For every integer k such that \max(1-A,B-N)\leq k\leq \min(N-A,B-1), paint (A+k,B-k) black.

In the grid after these operations, find the color of each square (i,j) such that P\leq i\leq Q and R\leq j\leq S.

Constraints

• 1 \leq N \leq 10^{18}
• 1 \leq A \leq N
• 1 \leq B \leq N
• 1 \leq P \leq Q \leq N
• 1 \leq R \leq S \leq N
• (Q-P+1)\times(S-R+1)\leq 3\times 10^5
• All values in input are integers.

Sample Input 1

5 3 2
1 5 1 5

Sample Output 1

...#.
#.#..
.#...
#.#..
...#.

The first operation paints the four squares (2,1), (3,2), (4,3), (5,4) black, and the second paints the four squares (4,1), (3,2), (2,3), (1,4) black.
Thus, the above output should be printed, since P=1, Q=5, R=1, S=5.

Sample Input 2

5 3 3
4 5 2 5

Sample Output 2

#.#.
...#

The operations paint the nine squares (1,1), (1,5), (2,2), (2,4), (3,3), (4,2), (4,4), (5,1), (5,5).
Thus, the above output should be printed, since P=4, Q=5, R=2, S=5.

Sample Input 3

1000000000000000000 999999999999999999 999999999999999999
999999999999999998 1000000000000000000 999999999999999998 1000000000000000000

Sample Output 3

#.#
.#.
#.#

Note that the input may not fit into a 32-bit integer type.