Problem Statement

You are given integers A and B between 0 and 255 (inclusive). Find a non-negative integer C such that A \text{ xor }C=B.

It can be proved that there uniquely exists such C, and it will be between 0 and 255 (inclusive).

Constraints

• 0\leq A,B \leq 255
• All values in input are integers.

Sample Input 1

3 6

Sample Output 1

5

When written in binary, 3 will be 11, and 5 will be 101. Thus, their \text{xor} will be 110 in binary, or 6 in decimal.

In short, 3 \text{ xor } 5 = 6, so the answer is 5.

Sample Input 2

10 12

Sample Output 2

6

Problem Statement

You are given a string S of length N consisting of three kinds of characters: ., |, and *. S contains exactly two | and exactly one *.

Determine whether the * is between the two |, and if so, print in; otherwise, print out.

More formally, determine whether one of the characters before the * is | and one of the characters after the * is |.

Constraints

• 3\leq N\leq 100
• N is an integer.
• S is a string of length N consisting of ., |, and *.
• S contains exactly two |.
• S contains exactly one *.

Sample Input 1

10
.|..*...|.

Sample Output 1

in

Between the two |, we have |..*...|, which contains *, so you should print in.

Sample Input 2

10
.|..|.*...

Sample Output 2

out

Between the two |, we have |..|, which does not contain *, so you should print out.

Sample Input 3

3
|*|

Sample Output 3

in

Problem Statement

You are given a string S. Find the lexicographically smallest string S' obtained by permuting the characters of S.

Here, for different two strings s = s_1 s_2 \ldots s_n and t = t_1 t_2 \ldots t_m, s \lt t holds lexicographically when one of the conditions below is satisfied.

• There is an integer i\ (1 \leq i \leq \min(n,m)) such that s_i \lt t_i and s_j=t_j for all integers j\ (1 \leq j \lt i).
• s_i = t_i for all integers i\ (1 \leq i \leq \min(n,m)), and n \lt m.

Constraints

• S is a string of length between 1 and 2 \times 10^5 (inclusive) consisting of lowercase English letters.

Sample Input 1

aba

Sample Output 1

aab

Three strings can be obtained by permuting aba:

• aba
• aab
• baa

The lexicographically smallest among them is aab.

Sample Input 2

zzzz

Sample Output 2

zzzz

Problem Statement

N people, person 1, person 2, \ldots, person N, are playing roulette. The outcome of a spin is one of the 37 integers from 0 to 36. For each i = 1, 2, \ldots, N, person i has bet on C_i of the 37 possible outcomes: A_{i, 1}, A_{i, 2}, \ldots, A_{i, C_i}.

The wheel has been spun, and the outcome is X. Print the numbers of all people who have bet on X with the fewest bets, in ascending order.

More formally, print all integers i between 1 and N, inclusive, that satisfy both of the following conditions, in ascending order:

• Person i has bet on X.
• For each j = 1, 2, \ldots, N, if person j has bet on X, then C_i \leq C_j.

Note that there may be no number to print (see Sample Input 2).

Constraints

• 1 \leq N \leq 100
• 1 \leq C_i \leq 37
• 0 \leq A_{i, j} \leq 36
• A_{i, 1}, A_{i, 2}, \ldots, A_{i, C_i} are all different for each i = 1, 2, \ldots, N.
• 0 \leq X \leq 36
• All input values are integers.

Sample Input 1

4
3
7 19 20
4
4 19 24 0
2
26 10
3
19 31 24
19

Sample Output 1

2
1 4

The wheel has been spun, and the outcome is 19. The people who has bet on 19 are person 1, person 2, and person 4, and the number of their bets are 3, 4, and 3, respectively. Therefore, among the people who has bet on 19, the ones with the fewest bets are person 1 and person 4.

Sample Input 2

3
1
1
1
2
1
3
0

Sample Output 2

0

The wheel has been spun and the outcome is 0, but no one has bet on 0, so there is no number to print.

Problem Statement

You are given a simple undirected graph with N vertices numbered 1 to N and M edges numbered 1 to M. Edge i connects vertex u_i and vertex v_i.
Find the number of connected components in this graph.

Notes

A simple undirected graph is a graph that is simple and has undirected edges.
A graph is simple if and only if it has no self-loop or multi-edge.

A subgraph of a graph is a graph formed from some of the vertices and edges of that graph.
A graph is connected if and only if one can travel between every pair of vertices via edges.
A connected component is a connected subgraph that is not part of any larger connected subgraph.

Constraints

• 1 \leq N \leq 100
• 0 \leq M \leq \frac{N(N - 1)}{2}
• 1 \leq u_i, v_i \leq N
• The given graph is simple.
• All values in the input are integers.

Sample Input 1

5 3
1 2
1 3
4 5

Sample Output 1

2

The given graph contains the following two connected components:

• a subgraph formed from vertices 1, 2, 3, and edges 1, 2;
• a subgraph formed from vertices 4, 5, and edge 3.

Sample Input 2

5 0

Sample Output 2

5

Sample Input 3

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

Sample Output 3

1

Problem Statement

In the xy-plane, we have N points numbered 1 through N.
Point i is at the coordinates (X_i,Y_i). Any two different points are at different positions.
Find the number of ways to choose three of these N points so that connecting the chosen points with segments results in a triangle with a positive area.

Constraints

• All values in input are integers.
• 3 \le N \le 300
• -10^9 \le X_i,Y_i \le 10^9
• (X_i,Y_i) \neq (X_j,Y_j) if i \neq j.

Sample Input 1

4
0 1
1 3
1 1
-1 -1

Sample Output 1

3

The figure below illustrates the points.

There are three ways to choose points that form a triangle: \{1,2,3\},\{1,3,4\},\{2,3,4\}.

Sample Input 2

20
224 433
987654321 987654321
2 0
6 4
314159265 358979323
0 0
-123456789 123456789
-1000000000 1000000000
124 233
9 -6
-4 0
9 5
-7 3
333333333 -333333333
-9 -1
7 -10
-1 5
324 633
1000000000 -1000000000
20 0

Sample Output 2

1124

Problem Statement

There is a sequence A = (A_0, A_1, \dots, A_{N - 1}) with N = 2^{20} terms. Initially, every term is -1.

Process Q queries in order. The i-th query (1 \leq i \leq Q) is described by an integer t_i such that t_i = 1 or t_i = 2, and another integer x_i, as follows.

• If t_i = 1, do the following in order.
  1. Define an integer h as h = x_i.
  2. While A_{h \bmod N} \neq -1, keep adding 1 to h. We can prove that this process ends after finite iterations under the Constraints of this problem.
  3. Replace the value of A_{h \bmod N} with x_i.
• If t_i = 2, print the value of A_{x_i \bmod N} at that time.

Here, for integers a and b, a \bmod b denotes the remainder when a is divided by b.

Constraints

• 1 \leq Q \leq 2 \times 10^5
• t_i \in \{ 1, 2 \} \, (1 \leq i \leq Q)
• 0 \leq x_i \leq 10^{18} \, (1 \leq i \leq Q)
• There is at least one i (1 \leq i \leq Q) such that t_i = 2.
• All values in input are integers.

Sample Input 1

4
1 1048577
1 1
2 2097153
2 3

Sample Output 1

1048577
-1

We have x_1 \bmod N = 1, so the first query sets A_1 = 1048577.

In the second query, initially we have h = x_2, for which A_{h \bmod N} = A_{1} \neq -1, so we add 1 to h. Now we have A_{h \bmod N} = A_{2} = -1, so this query sets A_2 = 1.

In the third query, we print A_{x_3 \bmod N} = A_{1} = 1048577.

In the fourth query, we print A_{x_4 \bmod N} = A_{3} = -1.

Note that, in this problem, N = 2^{20} = 1048576 is a constant and not given in input.

Problem Statement

There are N baskets numbered 1, 2, \ldots, N arranged in a circle.
For each 1\leq i \leq N-1, basket i+1 is to the immediate right of basket i, and basket 1 is to the immediate right of basket N.

Basket i now contains A_i apples.

Takahashi starts in front of basket 1 and repeats the following action.

• If the basket he is facing contains an apple, take one and eat it. Then, regardless of whether he has eaten an apple now, go on to the next basket to the immediate right.

Find the number of apples remaining in each basket when Takahashi has eaten exactly K apples in total.

Constraints

• 1 \leq N \leq 10^5
• 0 \leq A_i \leq 10^{12}
• 1 \leq K \leq 10^{12}
• There are at least K apples in total. That is, \sum_{i=1}^{N}A_i\geq K.
• All values in the input are integers.

Sample Input 1

3 3
1 3 0

Sample Output 1

0 1 0 

Takahashi will do the following.

• Basket 1, which he is facing, contains an apple, so he takes one and eats it. Then, he goes on to basket 2. Now, the baskets have 0,3,0 apples.
• Basket 2, which he is facing, contains an apple, so he takes one and eats it. Then, he goes on to basket 3. Now, the baskets have 0,2,0 apples.
• Basket 3, which he is facing, contains no apple. Then, he goes on to basket 1. Now, the baskets have 0,2,0 apples.
• Basket 1, which he is facing, contains no apple. Then, he goes on to basket 2. Now, the baskets have 0,2,0 apples.
• Basket 2, which he is facing, contains an apple, so he takes one and eats it. Then, he goes on to basket 3. Now, the baskets have 0,1,0 apple(s).

Sample Input 2

2 1000000000000
1000000000000 1000000000000

Sample Output 2

500000000000 500000000000 

Problem Statement

We have N cards. The i-th card has a string S_i written on it.

Find the lexicographically smallest string that can be obtained by choosing K of these cards and concatenating them in any order.

Constraints

• 1 \leq K \leq N \leq 50
• 1 \leq |S_i| \leq 50
• S_i consists of lowercase English letters.

Sample Input 1

4 3
ode
zaaa
r
atc

Sample Output 1

atcoder

Note that it is not possible to reverse or permute the string written on a card.
For example, ode written on the first card cannot be used as edo or deo.

Sample Input 2

5 2
z
z
zzz
z
zzzzzz

Sample Output 2

zz

There may be a pair i, j (i\neq j) such that S_i = S_j.