Problem Statement

This is the 214-th AtCoder Beginner Contest (ABC).

The ABCs so far have had the following number of problems.

• The 1-st through 125-th ABCs had 4 problems each.
• The 126-th through 211-th ABCs had 6 problems each.
• The 212-th through 214-th ABCs have 8 problems each.

Find the number of problems in the N-th ABC.

Constraints

• 1 \leq N \leq 214
• All values in input are integers.

Sample Input 1

214

Sample Output 1

8

Sample Input 2

1

Sample Output 2

4

Sample Input 3

126

Sample Output 3

6

Problem Statement

You are given N integers A_1,A_2,\dots, and A_N.

Find the sum of the N integers.

Constraints

• 1 \le N \le 100
• 1 \le A_i \le 100
• All values in the input are integers.

Sample Input 1

3
2 7 2

Sample Output 1

11

You are given three integers: 2, 7, and 2.

The answer is 2 + 7 + 2 = 11.

Sample Input 2

1
3

Sample Output 2

3

Problem Statement

Takahashi has N friends. They have nicknames: Friend 1, Friend 2, \ldots, Friend N.

One day, Takahashi accidentally let one of his friends, Friend X, learn his shameful secret.
For each i = 1, 2, \ldots, N, when Friend i learns the secret, he/she will share it with Friend A_i, if Friend A_i has not already learned it.

How many of Takahashi's friends will learn the secret in the end?

Constraints

• 2 \leq N \leq 10^5
• 1 \leq X \leq N
• 1 \leq A_i \leq N
• A_i \neq i
• All values in input are integers.

Sample Input 1

4 2
3 1 1 2

Sample Output 1

3

Takahashi's secret will be learned by Friend 1, Friend 2, and Friend 3, as follows.

• One day, Takahashi let Friend 2 learn the secret.
• Friend 2 shares it with Friend 1.
• Friend 1 shares it with Friend 3.

In the end, three of his friends learn the secret, so we print 3.

Sample Input 2

20 12
7 11 10 1 7 20 14 2 17 3 2 5 19 20 8 14 18 2 10 10

Sample Output 2

7

Problem Statement

Given an integer X between -10^{18} and 10^{18}, inclusive, print \left\lceil \dfrac{X}{10} \right\rceil.
Here, \left\lceil a \right\rceil denotes the smallest integer not less than a.

Constraints

• -10^{18} \leq X \leq 10^{18}
• X is an integer.

Sample Input 1

27

Sample Output 1

3

The integers not less than \frac{27}{10} = 2.7 are 3, 4, 5, \dots. Among these, the smallest is 3, so \left \lceil \frac{27}{10} \right \rceil = 3.

Sample Input 2

-13

Sample Output 2

-1

The integers not less than \frac{-13}{10} = -1.3 are all positive integers, 0, and -1. Among these, the smallest is -1, so \left \lceil \frac{-13}{10} \right \rceil = -1.

Sample Input 3

40

Sample Output 3

4

The smallest integer not less than \frac{40}{10} = 4 is 4 itself.

Sample Input 4

-20

Sample Output 4

-2

Sample Input 5

123456789123456789

Sample Output 5

12345678912345679

Problem Statement

You are given positive integers N and Q, and a string S of length N consisting of lowercase English letters.

Process Q queries. Each query is of one of the following two types.

• 1 x: Perform the following x times in a row: delete the last character of S and append it to the beginning.
• 2 x: Print the x-th character of S.

Constraints

• 2 \le N \le 5 \times 10^5
• 1 \le Q \le 5 \times 10^5
• 1 \le x \le N
• |S|=N
• S consists of lowercase English letters.
• At least one query in the format 2 x.
• N, Q, x are all integers.

Sample Input 1

3 3
abc
2 2
1 1
2 2

Sample Output 1

b
a

In the 1-st query, S is abc, so the 2-nd character b should be printed. In the 2-nd query, S is changed from abc to cab. In the 3-rd query, S is cab, so the 2-nd character a should be printed.

Sample Input 2

10 8
dsuccxulnl
2 4
2 7
1 2
2 7
1 1
1 2
1 3
2 5

Sample Output 2

c
u
c
u

Problem Statement

We have a grid with H horizontal rows and W vertical columns. (i, j) denotes the square at the i-th row from the top and j-th column from the left.
(i,j) has a character G_{i,j} written on it. G_{i,j} is U, D, L, or R.

You are initially at (1,1). You repeat the following operation until you cannot make a move.

Let (i,j) be the square you are currently at.
If G_{i,j} is U and i \neq 1, move to (i-1,j).
If G_{i,j} is D and i \neq H, move to (i+1,j).
If G_{i,j} is L and j \neq 1, move to (i,j-1).
If G_{i,j} is R and j \neq W, move to (i,j+1).
Otherwise, you cannot make a move.

Print the square you end up at when you cannot make a move.
If you indefinitely repeat moving, print -1 instead.

Constraints

• 1 \leq H, W \leq 500
• G_{i,j} is U, D, L, or R.
• H and W are integers.

Sample Input 1

2 3
RDU
LRU

Sample Output 1

1 3

You will move as (1, 1) \to (1, 2) \to (2, 2) \to (2, 3) \to (1, 3), ending up here, so the answer is (1, 3).

Sample Input 2

2 3
RRD
ULL

Sample Output 2

-1

You will indefinitely repeat moving as (1, 1) \to (1, 2) \to (1, 3) \to (2, 3) \to (2, 2) \to (2, 1) \to (1, 1) \to (1, 2) \to \dots, so -1 should be printed in this case.

Sample Input 3

9 44
RRDDDDRRRDDDRRRRRRDDDRDDDDRDDRDDDDDDRRDRRRRR
RRRDLRDRDLLLLRDRRLLLDDRDLLLRDDDLLLDRRLLLLLDD
DRDLRLDRDLRDRLDRLRDDLDDLRDRLDRLDDRLRRLRRRDRR
DDLRRDLDDLDDRLDDLDRDDRDDDDRLRRLRDDRRRLDRDRDD
RDLRRDLRDLLLLRRDLRDRRDRRRDLRDDLLLLDDDLLLLRDR
RDLLLLLRDLRDRLDDLDDRDRRDRLDRRRLDDDLDDDRDDLDR
RDLRRDLDDLRDRLRDLDDDLDDRLDRDRDLDRDLDDLRRDLRR
RDLDRRLDRLLLLDRDRLLLRDDLLLLLRDRLLLRRRRLLLDDR
RRRRDRDDRRRDDRDDDRRRDRDRDRDRRRRRRDDDRDDDDRRR

Sample Output 3

9 5

Problem Statement

There are N squares indexed 0 through (N-1) arranged in a line. Snuke is going to mark every square by the following procedure.

1. Mark square 0.
2. Repeat the following steps i - iii (N-1) times.
   1. Initialize a variable x with (A+D) \bmod N, where A is the index of the square marked last time.
   2. While square x is marked, repeat replacing x with (x+1) \bmod N.
   3. Mark square x.

Find the index of the square that Snuke marks for the K-th time.

Given T test cases, find the answer for each of them.

Constraints

• 1\leq T \leq 10^5
• 1\leq K\leq N \leq 10^9
• 1\leq D \leq 10^9
• All values in the input are integers.

Sample Input 1

9
4 2 1
4 2 2
4 2 3
4 2 4
5 8 1
5 8 2
5 8 3
5 8 4
5 8 5

Sample Output 1

0
2
1
3
0
3
1
4
2

If N=4 and D=2, Snuke marks the squares as follows.

1. Mark square 0.
2. (1-st iteration) Let x=(0+2)\bmod 4=2. Since square 2 is not marked, mark it.
   (2-nd iteration) Let x=(2+2)\bmod 4=0. Since square 0 is marked, let x=(0+1)\bmod 4=1. Since square 1 is not marked, mark it.
   (3-rd iteration) Let x=(1+2)\bmod 4=3. Since square 3 is not marked, mark it.

Problem Statement

There is a directed graph with N vertices numbered 1 to N and N edges.
The out-degree of every vertex is 1, and the edge from vertex i points to vertex a_i.
Count the number of pairs of vertices (u, v) such that vertex v is reachable from vertex u.

Here, vertex v is reachable from vertex u if there exists a sequence of vertices w_0, w_1, \dots, w_K of length K+1 that satisfies the following conditions. In particular, if u = v, it is always reachable.

• w_0 = u.
• w_K = v.
• For every 0 \leq i \lt K, there is an edge from vertex w_i to vertex w_{i+1}.

Constraints

• 1 \leq N \leq 2 \times 10^5
• 1 \leq a_i \leq N
• All input values are integers.

Sample Input 1

4
2 1 1 4

Sample Output 1

8

The vertices reachable from vertex 1 are vertices 1, 2.
The vertices reachable from vertex 2 are vertices 1, 2.
The vertices reachable from vertex 3 are vertices 1, 2, 3.
The vertex reachable from vertex 4 is vertex 4.
Therefore, the number of pairs of vertices (u, v) such that vertex v is reachable from vertex u is 8.
Note that the edge from vertex 4 is a self-loop, that is, it points to vertex 4 itself.

Sample Input 2

5
2 4 3 1 2

Sample Output 2

14

Sample Input 3

10
6 10 4 1 5 9 8 6 5 1

Sample Output 3

41

Problem Statement

We have a loaf of bread of length L, which we will cut and distribute to N children.
The i-th child (1\leq i\leq N) wants a loaf of length A_i.

Now, Takahashi will repeat the operation below to cut the loaf into lengths A_1, A_2, \ldots, A_N for the children.

Choose a loaf of length k and an integer x between 1 and k-1 (inclusive). Cut the loaf into two loaves of length x and k-x.
This operation incurs a cost of k regardless of the value of x.

Each child i must receive a loaf of length exactly A_i, but it is allowed to leave some loaves undistributed.

Find the minimum cost needed to distribute loaves to all children.

Constraints

• 2 \leq N \leq 2\times 10^5
• 1\leq A_i\leq 10^9
• A_1+A_2+\cdots+A_N\leq L\leq 10^{15}
• All values in input are integers.

Sample Input 1

5 7
1 2 1 2 1

Sample Output 1

16

Takahashi can cut the loaf for the children as follows.

• Choose the loaf of length 7 and x=3, cutting it into loaves of length 3 and 4 for a cost of 7.
• Choose the loaf of length 3 and x=1, cutting it into loaves of length 1 and 2 for a cost of 3. Give the former to the 1-st child.
• Choose the loaf of length 2 and x=1, cutting it into two loaves of length 1 for a cost of 2. Give them to the 3-rd and 5-th children.
• Choose the loaf of length 4 and x=2, cutting it into two loaves of length 2 for a cost of 4. Give them to the 2-nd and 4-th children.

This incurs a cost of 7+3+2+4=16, which is the minimum possible. There will be no leftover loaves.

Sample Input 2

3 1000000000000000
1000000000 1000000000 1000000000

Sample Output 2

1000005000000000

Note that each child i must receive a loaf of length exactly A_i.