Problem Statement

The number pi to the 100-th decimal place is

3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679.

You are given an integer N between 1 and 100, inclusive.

Print the value of pi to the N-th decimal place.

More precisely, truncate the value of pi to N decimal places and print the result without removing the trailing 0s.

Constraints

• 1\leq N\leq 100
• N is an integer.

Sample Input 1

2

Sample Output 1

3.14

Truncating the value of pi to 2 decimal places results in 3.14. Thus, you should print 3.14.

Sample Input 2

32

Sample Output 2

3.14159265358979323846264338327950

Do not remove the trailing 0s.

Sample Input 3

100

Sample Output 3

3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679

Problem Statement

A sport event is held in June of every year whose remainder when divided by 4 is 2.
Suppose that it is now January of the year Y. In what year will this sport event be held next time?

Constraints

• 2000 \leq Y \leq 3000
• Y is an integer.

Sample Input 1

2022

Sample Output 1

2022

The remainder when 2022 is divided by 4 is 2, so if it is now January of 2022, the next games will be held in June of the same year.

Sample Input 2

2023

Sample Output 2

2026

Sample Input 3

3000

Sample Output 3

3002

Problem Statement

Iroha has a sequence of positive integers A = (A_1, A_2, \dots, A_N) of length N (N \ge 1).
She generated a string S using A as follows:

• Start with S = |.
• For i = 1, 2, \dots, N, perform the following operations in order:
  • Append A_i copies of - to the end of S.
  • Then, append one | to the end of S.

Given the generated string S, reconstruct the sequence A.

Constraints

• S is a string of length between 3 and 100, inclusive, generated by the method in the problem statement.
• A is a sequence of positive integers of length at least 1.

Sample Input 1

|---|-|----|-|-----|

Sample Output 1

3 1 4 1 5

S = |---|-|----|-|-----| is generated by A = (3, 1, 4, 1, 5).

Sample Input 2

|----------|

Sample Output 2

10

Sample Input 3

|-|-|-|------|

Sample Output 3

1 1 1 6

Problem Statement

You are given a sequence of N positive integers A = (A_1, A_2, \dots ,A_N). Takahashi repeats the following operation until A contains one or fewer positive elements:

• Sort A in descending order. Then, decrease both A_1 and A_2 by 1.

Find the number of times he performs this operation.

Constraints

• 2 \leq N \leq 100
• 1 \leq A_i \leq 100
• All input values are integers.

Sample Input 1

4
1 2 3 3

Sample Output 1

4

The process goes as follows:

• After the 1st operation, A is (2, 2, 2, 1).
• After the 2nd operation, A is (1, 1, 2, 1).
• After the 3rd operation, A is (1, 0, 1, 1).
• After the 4th operation, A is (0, 0, 1, 0). A no longer contains more than one positive elements, so the process ends here.

Sample Input 2

3
1 1 100

Sample Output 2

2

Problem Statement

The AtCoder Kingdom holds a festival for N days. On M of these days, namely on the A_1-th, A_2-th, \dots, A_M-th days, fireworks will be launched. It is guaranteed that fireworks will be launched on the last day of the festival. (In other words, A_M=N is guaranteed.)

For each i=1,2,\dots,N, solve the following problem.

• How many days later from the i-th day will fireworks be launched for the first time on or after the i-th day? If fireworks are launched on the i-th day, it is considered to be 0 days later.

Constraints

• 1 \le M \le N \le 2 \times 10^5
• 1 \le A_1 < A_2 < \dots < A_M = N
• All input values are integers.

Sample Input 1

3 2
2 3

Sample Output 1

1
0
0

The kingdom holds a festival for 3 days, and fireworks are launched on the 2-nd and 3-rd days.

• From the 1-st day, the first time fireworks are launched is the 2-nd day of the festival, which is 1 day later.
• From the 2-nd day, the first time fireworks are launched is the 2-nd day of the festival, which is 0 days later.
• From the 3-rd day, the first time fireworks are launched is the 3-rd day of the festival, which is 0 days later.

Sample Input 2

8 5
1 3 4 7 8

Sample Output 2

0
1
0
0
2
1
0
0

Problem Statement

Among the positive integers that consist of 0's and 2's when written in base 10, find the K-th smallest integer.

Constraints

• K is an integer between 1 and 10^{18} (inclusive).

Sample Input 1

3

Sample Output 1

22

The positive integers that consist of 0's and 2's when written in base 10 are 2,20,22,\dots in ascending order.
The (K=) 3-rd of them, which is 22, should be printed.

Sample Input 2

11

Sample Output 2

2022

Sample Input 3

923423423420220108

Sample Output 3

220022020000202020002022022000002020002222002200002022002200

Note that the exact value of the answer must be printed as an integer, even if it is big.

Problem Statement

On a certain planet, there are N aliens, all of whom are minors.

The i-th alien currently has A_i stones, and will become an adult exactly i years later.

When someone becomes an adult on this planet, every adult who has at least one stone gives exactly one stone as a congratulatory gift to the alien who has just become an adult.

Find how many stones each alien will have after N years.

Assume that no new aliens will be born in the future.

Constraints

• 1 \leq N \leq 5 \times 10^5
• 0 \leq A_i \leq 5 \times 10^5
• All input values are integers.

Sample Input 1

4
5 0 9 3

Sample Output 1

2 0 10 5

Let C_i be the number of stones that the i-th alien has at a given time.

Initially, (C_1, C_2, C_3, C_4) = (5, 0, 9, 3).

After 1 year, (C_1, C_2, C_3, C_4) = (5, 0, 9, 3).

After 2 years, (C_1, C_2, C_3, C_4) = (4, 1, 9, 3).

After 3 years, (C_1, C_2, C_3, C_4) = (3, 0, 11, 3).

After 4 years, (C_1, C_2, C_3, C_4) = (2, 0, 10, 5).

Sample Input 2

5
4 6 7 2 5

Sample Output 2

0 4 7 4 9

Sample Input 3

10
2 9 1 2 0 4 6 7 1 5

Sample Output 3

0 2 0 0 0 4 7 10 4 10

Problem Statement

10^{100} potatoes are coming from a conveyor belt one by one. The weights of the potatoes are described by a sequence W = (W_0, \dots, W_{N-1}) of length N: the weight of the i-th potato coming is W_{(i-1) \bmod N}, where (i-1) \bmod N denotes the remainder when i - 1 is divided by N.

Takahashi will prepare an empty box and then pack the potatoes in order, as follows.

• Pack the incoming potato into the box. If the total weight of the potatoes in the box is now X or greater, seal that box and prepare a new empty box.

You are given Q queries. In the i-th query (1 \leq i \leq Q), given a positive integer K_i, find the number of potatoes in the K_i-th box to be sealed. It can be proved that, under the Constraints of the problem, there will be at least K_i sealed boxes.

Constraints

• 1 \leq N, Q \leq 2 \times 10^5
• 1 \leq X \leq 10^9
• 1 \leq W_i \leq 10^9 \, (0 \leq i \leq N - 1)
• 1 \leq K_i \leq 10^{12} \, (1 \leq i \leq Q)
• All values in input are integers.

Sample Input 1

3 2 5
3 4 1
1
2

Sample Output 1

2
3

Before sealing the 2-nd box, Takahashi will do the following:

• Prepare an empty box.
• Pack the 1-st potato into the box. Now, the total weight of potatoes in the box is 3.
• Pack the 2-nd potato into the box. Now, the total weight of potatoes in the box is 3 + 4 = 7, which is not less than X = 5, so seal this box.
• Prepare a new empty box.
• Pack the 3-rd potato into the box. Now, the total weight of potatoes in the box is 1.
• Pack the 4-th potato into the box. Now, the total weight of potatoes in the box is 1 + 3 = 4.
• Pack the 5-th potato into the box. Now, the total weight of potatoes in the box is 1 + 3 + 4 = 8, which is not less than X = 5, so seal this box.

The 1-st box sealed contains 2 potatoes, and the 2-nd box sealed contains 3 potatoes.

Sample Input 2

10 5 20
5 8 5 9 8 7 4 4 8 2
1
1000
1000000
1000000000
1000000000000

Sample Output 2

4
5
5
5
5

Problem Statement

Let the similarity f(X,Y) between two strings X and Y be the length of their longest common prefix.
For example, the similarity between abc and axbc is 1, and the similarity between aaa and aaaa is 3.

You are given a string S of length N. Let S_i be the suffix of S beginning with the i-th character of S. For each k=1,\ldots,N, find f(S_k,S_1)+f(S_k,S_2)+\ldots+f(S_k,S_N).

Constraints

• 1 \leq N \leq 10^6
• S is a string of length N consisting of lowercase English letters.

Sample Input 1

3
abb

Sample Output 1

3
3
2

S_1 is abb, S_2 is bb, and S_3 is b.

• For k=1: f(S_1,S_1)+f(S_1,S_2)+f(S_1,S_3)=3+0+0=3.
• For k=2: f(S_2,S_1)+f(S_2,S_2)+f(S_2,S_3)=0+2+1=3.
• For k=3: f(S_3,S_1)+f(S_3,S_2)+f(S_3,S_3)=0+1+1=2.

Sample Input 2

11
mississippi

Sample Output 2

11
16
14
12
13
11
9
7
4
3
4