Problem Statement

You are given an integer N and a sequence A=(A _ 1,A _ 2,\ldots,A _ N) of length N.

Given Q queries, process them in the given order. Each query is of one of the following two kinds:

• 1 k x : set the value A _ k to x.
• 2 k : print the value A _ k.

Constraints

• 1 \leq N \leq 10 ^ 5
• 1 \leq Q \leq 10 ^ 5
• 0 \leq A _ i \leq 10 ^ 9\ (1\leq i\leq N)
• 1\leq k\leq N for all queries.
• 0\leq x\leq 10 ^ 9 for all queries of the first kind.
• There is at least one query of the second kind.
• All values in the input are integers.

Sample Input 1

3
1 3 5
7
2 2
2 3
1 3 0
2 3
1 2 8
2 2
2 1

Sample Output 1

3
5
0
8
1

Initially, A=(1,3,5).

• For the 1-st query, A=(1,3,5), where A _ 2=3, so 3 should be printed.
• For the 2-nd query, A=(1,3,5), where A _ 3=5, so 5 should be printed.
• The 3-rd query sets the value A _ 3 to 0, making A=(1,3,0).
• For the 4-th query, A=(1,3,0), where A _ 3=0, so 0 should be printed.
• The 5-th query sets the value A _ 2 to 8, making A=(1,8,0).
• For the 6-th query, A=(1,8,0), where A _ 2=8, so 8 should be printed.
• For the 7-th query, A=(1,8,0), where A _ 1=1, so 1 should be printed.

Sample Input 2

5
22 2 16 7 30
10
1 4 0
1 5 0
2 2
2 3
2 4
2 5
1 4 100
1 5 100
2 3
2 4

Sample Output 2

2
16
0
0
16
100

Sample Input 3

7
478 369 466 343 541 42 165
20
2 1
1 7 729
1 6 61
1 6 838
1 3 319
1 4 317
2 4
1 1 673
1 3 176
1 5 250
1 1 468
2 6
1 7 478
1 5 595
2 6
1 6 599
1 6 505
2 3
2 5
2 1

Sample Output 3

478
317
838
838
176
595
468

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

There are N stations on a certain line operated by AtCoder Railway. The i-th station (1 \leq i \leq N) from the starting station is named S_i.

Local trains stop at all stations, while express trains may not. Specifically, express trains stop at only M \, (M \leq N) stations, and the j-th stop (1 \leq j \leq M) is the station named T_j.
Here, it is guaranteed that T_1 = S_1 and T_M = S_N, that is, express trains stop at both starting and terminal stations.

For each of the N stations, determine whether express trains stop at that station.

Constrains

• 2 \leq M \leq N \leq 10^5
• N and M are integers.
• S_i (1 \leq i \leq N) is a string of length between 1 and 10 (inclusive) consisting of lowercase English letters.
• S_i \neq S_j \, (i \neq j)
• T_1 = S_1 and T_M = S_N.
• (T_1, \dots, T_M) is obtained by removing zero or more strings from (S_1, \dots, S_N) and lining up the remaining strings without changing the order.

Sample Input 1

5 3
tokyo kanda akiba okachi ueno
tokyo akiba ueno

Sample Output 1

Yes
No
Yes
No
Yes

Sample Input 2

7 7
a t c o d e r
a t c o d e r

Sample Output 2

Yes
Yes
Yes
Yes
Yes
Yes
Yes

Express trains may stop at all stations.

Problem Statement

There are N creatures standing in a circle, called Snuke 1, 2, ..., N in counter-clockwise order.

When Snuke i (1 \leq i \leq N) receives a gem at time t, S_i units of time later, it will hand that gem to Snuke i+1 at time t+S_i. Here, Snuke N+1 is Snuke 1.

Additionally, Takahashi will hand a gem to Snuke i at time T_i.

For each i (1 \leq i \leq N), find the time when Snuke i receives a gem for the first time. Assume that it takes a negligible time to hand a gem.

Constraints

• 1 \leq N \leq 200000
• 1 \leq S_i,T_i \leq 10^9
• All values in input are integers.

Sample Input 1

3
4 1 5
3 10 100

Sample Output 1

3
7
8

We will list the three Snuke's and Takahashi's actions up to time 13 in chronological order.

Time 3: Takahashi hands a gem to Snuke 1.

Time 7: Snuke 1 hands a gem to Snuke 2.

Time 8: Snuke 2 hands a gem to Snuke 3.

Time 10: Takahashi hands a gem to Snuke 2.

Time 11: Snuke 2 hands a gem to Snuke 3.

Time 13: Snuke 3 hands a gem to Snuke 1.

After that, they will continue handing gems, though it will be irrelevant to the answer.

Sample Input 2

4
100 100 100 100
1 1 1 1

Sample Output 2

1
1
1
1

Note that the values S_i and T_i may not be distinct.

Sample Input 3

4
1 2 3 4
1 2 4 7

Sample Output 3

1
2
4
7

Note that a Snuke may perform multiple transactions simultaneously. Particularly, a Snuke may receive gems simultaneously from Takahashi and another Snuke.

Sample Input 4

8
84 87 78 16 94 36 87 93
50 22 63 28 91 60 64 27

Sample Output 4

50
22
63
28
44
60
64
27

Problem Statement

We have a positive integer a. Additionally, there is a blackboard with a number written in base 10.
Let x be the number on the blackboard. Takahashi can do the operations below to change this number.

• Erase x and write x multiplied by a, in base 10.
• See x as a string and move the rightmost digit to the beginning.
  This operation can only be done when x \geq 10 and x is not divisible by 10.

For example, when a = 2, x = 123, Takahashi can do one of the following.

• Erase x and write x \times a = 123 \times 2 = 246.
• See x as a string and move the rightmost digit 3 of 123 to the beginning, changing the number from 123 to 312.

The number on the blackboard is initially 1. What is the minimum number of operations needed to change the number on the blackboard to N? If there is no way to change the number to N, print -1.

Constraints

• 2 \leq a \lt 10^6
• 2 \leq N \lt 10^6
• All values in input are integers.

Sample Input 1

3 72

Sample Output 1

4

We can change the number on the blackboard from 1 to 72 in four operations, as follows.

• Do the operation of the first type: 1 \to 3.
• Do the operation of the first type: 3 \to 9.
• Do the operation of the first type: 9 \to 27.
• Do the operation of the second type: 27 \to 72.

It is impossible to reach 72 in three or fewer operations, so the answer is 4.

Sample Input 2

2 5

Sample Output 2

-1

It is impossible to change the number on the blackboard to 5.

Sample Input 3

2 611

Sample Output 3

12

There is a way to change the number on the blackboard to 611 in 12 operations: 1 \to 2 \to 4 \to 8 \to 16 \to 32 \to 64 \to 46 \to 92 \to 29 \to 58 \to 116 \to 611, which is the minimum possible.

Sample Input 4

2 767090

Sample Output 4

111