Problem Statement

AtCoder Inc. sells T-shirts with its logo.

You are given Takahashi's schedule for N days as a string S of length N consisting of 0, 1, and 2.
Specifically, for an integer i satisfying 1\leq i\leq N,

• if the i-th character of S is 0, he has no plan scheduled for the i-th day;
• if the i-th character of S is 1, he plans to go out for a meal on the i-th day;
• if the i-th character of S is 2, he plans to attend a competitive programming event on the i-th day.

Takahashi has M plain T-shirts, all washed and ready to wear just before the first day.
In addition, to be able to satisfy the following conditions, he will buy several AtCoder logo T-shirts.

• On days he goes out for a meal, he will wear a plain or logo T-shirt.
• On days he attends a competitive programming event, he will wear a logo T-shirt.
• On days with no plans, he will not wear any T-shirts. Also, he will wash all T-shirts worn at that point. He can wear them again from the next day onwards.
• Once he wears a T-shirt, he cannot wear it again until he washes it.

Determine the minimum number of T-shirts he needs to buy to be able to wear appropriate T-shirts on all scheduled days during the N days. If he does not need to buy new T-shirts, print 0.
Assume that the purchased T-shirts are also washed and ready to use just before the first day.

Constraints

• 1\leq M\leq N\leq 1000
• S is a string of length N consisting of 0, 1, and 2.
• N and M are integers.

Sample Input 1

6 1
112022

Sample Output 1

2

If Takahashi buys two logo T-shirts, he can wear T-shirts as follows:

• On the first day, he wears a logo T-shirt to go out for a meal.
• On the second day, he wears a plain T-shirt to go out for a meal.
• On the third day, he wears a logo T-shirt to attend a competitive programming event.
• On the fourth day, he has no plans, so he washes all the worn T-shirts. This allows him to reuse the T-shirts worn on the first, second, and third days.
• On the fifth day, he wears a logo T-shirt to attend a competitive programming event.
• On the sixth day, he wears a logo T-shirt to attend a competitive programming event.

If he buys one or fewer logo T-shirts, he cannot use T-shirts to meet the conditions no matter what. Hence, print 2.

Sample Input 2

3 1
222

Sample Output 2

3

Sample Input 3

2 1
01

Sample Output 3

0

He does not need to buy new T-shirts.

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

There are N+Q points A_1,\dots,A_N,B_1,\dots,B_Q on a number line, where point A_i has a coordinate a_i and point B_j has a coordinate b_j.

For each j=1,2,\dots,Q, answer the following question:

• Let X be the point among A_1,A_2,\dots,A_N that is the k_j-th closest to point B_j. Find the distance between points X and B_j. More formally, let d_i be the distance between points A_i and B_j. Sort (d_1,d_2,\dots,d_N) in ascending order to get the sequence (d_1',d_2',\dots,d_N'). Find d_{k_j}'.

Constraints

• 1 \leq N, Q \leq 10^5
• -10^8 \leq a_i, b_j \leq 10^8
• 1 \leq k_j \leq N
• All input values are integers.

Sample Input 1

4 3
-3 -1 5 6
-2 3
2 1
10 4

Sample Output 1

7
3
13

Let us explain the first query.

The distances from points A_1, A_2, A_3, A_4 to point B_1 are 1, 1, 7, 8, respectively, so the 3rd closest to point B_1 is point A_3. Therefore, print the distance between point A_3 and point B_1, which is 7.

Sample Input 2

2 2
0 0
0 1
0 2

Sample Output 2

0
0

There may be multiple points with the same coordinates.

Sample Input 3

10 5
-84 -60 -41 -100 8 -8 -52 -62 -61 -76
-52 5
14 4
-2 6
46 2
26 7

Sample Output 3

11
66
59
54
88

Problem Statement

You are given a sequence A=(A_0,A_1,\ldots,A_{N-1}) of length N.
There is an initially empty dish. Takahashi is going to repeat the following operation K times.

• Let X be the number of candies on the dish. He puts A_{(X\bmod N)} more candies on the dish. Here, X\bmod N denotes the remainder when X is divided by N.

Find how many candies are on the dish after the K operations.

Constraints

• 2 \leq N \leq 2\times 10^5
• 1 \leq K \leq 10^{12}
• 1 \leq A_i\leq 10^6
• All values in input are integers.

Sample Input 1

5 3
2 1 6 3 1

Sample Output 1

11

The number of candies on the dish transitions as follows.

• In the 1-st operation, we have X=0, so A_{(0\mod 5)}=A_0=2 more candies will be put on the dish.
• In the 2-nd operation, we have X=2, so A_{(2\mod 5)}=A_2=6 more candies will be put on the dish.
• In the 3-rd operation, we have X=8, so A_{(8\mod 5)}=A_3=3 more candies will be put on the dish.

Thus, after the 3 operations, there will be 11 candies on the dish. Note that you must not print the remainder divided by N.

Sample Input 2

10 1000000000000
260522 914575 436426 979445 648772 690081 933447 190629 703497 47202

Sample Output 2

826617499998784056

The answer may not fit into a 32-bit integer type.

Problem Statement

You are given an integer K. For a set S that is initially empty, process Q queries of the following two types in order:

• 1 x: An integer x is given. If x is in S, remove x from S. Otherwise, add x to S.
• 2 x: An integer x that is in S is given. Consider a graph where the vertices are the numbers in S, and there is an edge between two numbers if and only if the absolute difference between them is at most K. Print the count of vertices in the connected component that contains x.

Constraints

• 1 \leq Q \leq 2\times 10^5
• 0 \leq K \leq 10^{18}
• For each query, 1 \leq x \leq 10^{18}.
• For each query of the second type, the given x is in S at that point.
• All input values are integers.

Sample Input 1

7 5
1 3
1 10
2 3
1 7
2 3
1 10
2 3

Sample Output 1

1
3
2

The query processing proceeds as follows:

• In the first query, 3 is added to S, resulting in S=\{3\}.
• In the second query, 10 is added to S, resulting in S=\{3,10\}.
• In the third query, consider a graph with vertices 3 and 10 and no edges. The connected component containing 3 has a size of 1, so print 1.
• In the fourth query, 7 is added to S, resulting in S=\{3,7,10\}.
• In the fifth query, consider a graph with vertices 3, 7, and 10, with edges between 3 and 7, and 7 and 10. The connected component containing 3 has a size of 3, so print 3.
• In the sixth query, 10 is removed from S, resulting in S=\{3,7\}.
• In the seventh query, consider a graph with vertices 3 and 7, with an edge between them. The connected component containing 3 has a size of 2, so print 2.

Sample Input 2

11 1000000000000000000
1 1
1 100
1 10000
1 1000000
1 100000000
1 10000000000
1 1000000000000
1 100000000000000
1 10000000000000000
1 1000000000000000000
2 1

Sample Output 2

10

Sample Input 3

8 0
1 1
1 2
2 1
1 1
1 2
1 1
1 2
2 1

Sample Output 3

1
1