Problem Statement

You are given a positive integer D.

Find the area of a circle with diameter D.

Constraints

• 1\le D\le 100
• The input value is an integer.

Sample Input 1

2

Sample Output 1

3.141592653589793

The area of a circle with diameter 2 is 3.141592653589793\ldots.

Sample Input 2

7

Sample Output 2

38.48451000647496

Sample Input 3

98

Sample Output 3

7542.9639612690935

Problem Statement

One day, Takahashi got up at exactly B minutes past A o'clock (in 24-hour clock), and Aoki got up at exactly D minutes and 1 second past C o'clock.
If Takahashi got up earlier than Aoki, print Takahashi; otherwise, print Aoki.

Constraints

• 0 \leq A \leq 23
• 0 \leq B \leq 59
• 0 \leq C \leq 23
• 0 \leq D \leq 59
• All values in input are integers.

Sample Input 1

7 0 6 30

Sample Output 1

Aoki

Takahashi got up at 7 sharp, and Aoki got up at 30 minutes and 1 second past 6 o'clock. Aoki was the first to get up, so Aoki should be printed.

Sample Input 2

7 30 7 30

Sample Output 2

Takahashi

Takahashi got up at exactly half past 7, and Aoki got up at 30 minutes and 1 second past 7 o'clock. Just by one second, Takahashi was the first to get up, so Takahashi should be printed.

Sample Input 3

0 0 23 59

Sample Output 3

Takahashi

0:00 in a day is one minute before 0:01, not one minute past 23:59 ("24:00"). Thus, Takahashi was the first to get up, so Takahashi should be printed.

Problem Statement

I begin with T and end with T, and I am full of T. What am I?

For a string t, define the filling rate as follows:

• If the first and last characters of t are both t and |t| \geq 3: Let x be the number of t in t. Then the filling rate of t is \displaystyle\frac{x-2}{|t|-2}, where |t| denotes the length of t.
• Otherwise: the filling rate of t is 0.

You are given a string S. Find the maximum possible filling rate of a substring of S.

Constraints

• 1 \leq |S| \leq 100
• S is a string consisting of lowercase English letters.

Sample Input 1

attitude

Sample Output 1

0.50000000000000000

ttit is a substring of S, and its filling rate is \displaystyle\frac{3-2}{4-2} = \frac{1}{2}.

There is no substring with a filling rate greater than \frac{1}{2}, so the answer is \frac{1}{2}.

Sample Input 2

ottottott

Sample Output 2

0.66666666666666667

ttottott is a substring of S, and its filling rate is \displaystyle\frac{6-2}{8-2} = \frac{2}{3}.

There is no substring with a filling rate greater than \frac{2}{3}, so the answer is \frac{2}{3}.

Sample Input 3

coffeecup

Sample Output 3

0.00000000000000000

ff is a substring of S, and its filling rate is 0.

There is no substring with a filling rate greater than 0, so the answer is 0.

Problem Statement

You are given a string T consisting of lowercase English letters and ?, and a string U consisting of lowercase English letters.

The string T is obtained by taking some lowercase-only string S and replacing exactly four of its characters with ?.

Determine whether it is possible that the original string S contained U as a contiguous substring.

Constraints

• T is a string of length between 4 and 10, inclusive, consisting of lowercase letters and ?.
• T contains exactly four occurrences of ?.
• U is a string of length between 1 and |T|, inclusive, consisting of lowercase letters.

Sample Input 1

tak??a?h?
nashi

Sample Output 1

Yes

For example, if S is takanashi, it contains nashi as a contiguous substring.

Sample Input 2

??e??e
snuke

Sample Output 2

No

No matter what characters replace the ?s in T, S cannot contain snuke as a contiguous substring.

Sample Input 3

????
aoki

Sample Output 3

Yes

Problem Statement

You are given strictly increasing sequences of length N and M: A=(A _ 1,A _ 2,\ldots,A _ N) and B=(B _ 1,B _ 2,\ldots,B _ M). Here, A _ i\neq B _ j for every i and j (1\leq i\leq N,1\leq j\leq M).

Let C=(C _ 1,C _ 2,\ldots,C _ {N+M}) be a strictly increasing sequence of length N+M that results from the following procedure.

• Let C be the concatenation of A and B. Formally, let C _ i=A _ i for i=1,2,\ldots,N, and C _ i=B _ {i-N} for i=N+1,N+2,\ldots,N+M.
• Sort C in ascending order.

For each of A _ 1,A _ 2,\ldots,A _ N, B _ 1,B _ 2,\ldots,B _ M, find its position in C. More formally, for each i=1,2,\ldots,N, find k such that C _ k=A _ i, and for each j=1,2,\ldots,M, find k such that C _ k=B _ j.

Constraints

• 1\leq N,M\leq 10^5
• 1\leq A _ 1\lt A _ 2\lt\cdots\lt A _ N\leq 10^9
• 1\leq B _ 1\lt B _ 2\lt\cdots\lt B _ M\leq 10^9
• A _ i\neq B _ j for every i and j (1\leq i\leq N,1\leq j\leq M).
• All values in the input are integers.

Sample Input 1

4 3
3 14 15 92
6 53 58

Sample Output 1

1 3 4 7
2 5 6

C will be (3,6,14,15,53,58,92). Here, the 1-st, 3-rd, 4-th, 7-th elements are from A=(3,14,15,92), and the 2-nd, 5-th, 6-th elements are from B=(6,53,58).

Sample Input 2

4 4
1 2 3 4
100 200 300 400

Sample Output 2

1 2 3 4
5 6 7 8

Sample Input 3

8 12
3 4 10 15 17 18 22 30
5 7 11 13 14 16 19 21 23 24 27 28

Sample Output 3

1 2 5 9 11 12 15 20
3 4 6 7 8 10 13 14 16 17 18 19

Problem Statement

You are given two sequences: A=(A_1,A_2, \ldots ,A_N) consisting of N positive integers, and B=(B_1, \ldots ,B_M) consisting of M positive integers.

Find the minimum difference of an element of A and an element of B, that is, \displaystyle \min_{ 1\leq i\leq N}\displaystyle\min_{1\leq j\leq M} \lvert A_i-B_j\rvert.

Constraints

• 1 \leq N,M \leq 2\times 10^5
• 1 \leq A_i \leq 10^9
• 1 \leq B_i \leq 10^9
• All values in input are integers.

Sample Input 1

2 2
1 6
4 9

Sample Output 1

2

Here is the difference for each of the four pair of an element of A and an element of B: \lvert 1-4\rvert=3, \lvert 1-9\rvert=8, \lvert 6-4\rvert=2, and \lvert 6-9\rvert=3. We should print the minimum of these values, or 2.

Sample Input 2

1 1
10
10

Sample Output 2

0

Sample Input 3

6 8
82 76 82 82 71 70
17 39 67 2 45 35 22 24

Sample Output 3

3

Problem Statement

There is a pond with a circumference of M, and on its shore stand one hut and N people.
For a real number x (0\leq x <M), define point x as the location that is x distance clockwise from the hut.
The i-th person is at point A_i. Multiple people may be standing at the same location.

Additionally, an integer C not greater than N is given. For i=0,1,\ldots,M-1, define X_i as follows:

1. Takahashi starts at point (i+0.5) and begins moving clockwise.
2. Takahashi continues moving (clockwise) as long as the total number of people he has met is less than C, and stops when it becomes C or more. Here, "meeting a person at point y" means that Takahashi reaches point y.
3. Let X_i be the number of people Takahashi met before stopping. Here, if there are multiple people at the point where Takahashi stopped, all the people there are counted as people he met, and particularly, X_i may be greater than C.

Find the sum of X_i over i=0,1,\ldots,M-1, that is, \displaystyle\sum_{i=0}^{M-1} X_i.

Constraints

• 1\leq N\leq 5\times 10^5
• 1\leq M\leq 10^{12}
• 0\leq A_i\leq M-1
• 1\leq C\leq N
• All input values are integers.

Sample Input 1

5 3 2
1 2 1 0 1

Sample Output 1

9

When i=0, Takahashi starts at point 0.5 and moves clockwise. Then, the following happens:

• At point 1, he meets the 1st, 3rd, and 5th people, a total of three people, and the total number of people met so far is 3. This is not less than C=2, so Takahashi stops there. Therefore, X_0=3.

When i=1, Takahashi starts at point 1.5 and moves clockwise. Then, the following happens:

• At point 2, he meets the 2nd person. The total number of people met so far is 1, so he continues moving.
• At point 0, he meets the 4th person, and the total number of people met so far is 2. This is not less than C=2, so Takahashi stops there. Therefore, X_1=2.

When i=2, Takahashi starts at point 2.5 and moves clockwise. Then, the following happens:

• At point 0, he meets the 4th person. The total number of people met so far is 1, so he continues moving.
• At point 1, he meets the 1st, 3rd, and 5th people, a total of three people, and the total number of people met so far is 4. This is not less than C=2, so Takahashi stops there. Therefore, X_2=4.

Therefore, the answer is X_0+X_1+X_2=3+2+4=9.

Sample Input 2

1 1000000000000 1
1

Sample Output 2

1000000000000

Regardless of the starting position, Takahashi stops when he meets the only person standing around the pond, who is at point 1.
Therefore, X_i=1 regardless of i, and the answer is 10^{12}.

Problem Statement

You are given a sequence of length M consisting of integers between 1 and N-1, inclusive: A=(A_1,A_2,\dots,A_M). Answer the following question for i=1, 2, \dots, M.

• There is a sequence B=(B_1,B_2,\dots,B_N). Initially, we have B_j=j for each j. Let us perform the following operation for k=1, 2, \dots, i-1, i+1, \dots, M in this order (in other words, for integers k between 1 and M except i in ascending order).
  • Swap the values of B_{A_k} and B_{A_k+1}.
• After all the operations, let S_i be the value of j such that B_j=1. Find S_i.

Constraints

• 2 \leq N \leq 2\times 10^5
• 1 \leq M \leq 2\times 10^5
• 1 \leq A_i \leq N-1\ (1\leq i \leq M)
• All values in the input are integers.

Sample Input 1

5 4
1 2 3 2

Sample Output 1

1
3
2
4

For i = 2, the operations change B as follows.

• Initially, B = (1,2,3,4,5).
• Perform the operation for k=1. That is, swap the values of B_1 and B_2, making B = (2,1,3,4,5).
• Perform the operation for k=3. That is, swap the values of B_3 and B_4, making B = (2,1,4,3,5).
• Perform the operation for k=4. That is, swap the values of B_2 and B_3, making B = (2,4,1,3,5).

After all the operations, we have B_3=1, so S_2 = 3.

Similarly, we have the following.

• For i=1: performing the operation for k=2,3,4 in this order makes B=(1,4,3,2,5), so S_1=1.
• For i=3: performing the operation for k=1,2,4 in this order makes B=(2,1,3,4,5), so S_3=2.
• For i=4: performing the operation for k=1,2,3 in this order makes B=(2,3,4,1,5), so S_4=4.

Sample Input 2

3 3
2 2 2

Sample Output 2

1
1
1

Sample Input 3

10 10
1 1 1 9 4 4 2 1 3 3

Sample Output 3

2
2
2
3
3
3
1
3
4
4

Problem Statement

There are N rooms numbered 1, 2, \ldots, N, each with one person living in it, and M corridors connecting two different rooms. The i-th corridor connects room U_i and room V_i with a length of W_i.

One day (we call this day 0), the K people living in rooms A_1, A_2, \ldots, A_K got (newly) infected with a virus. Furthermore, on the i-th of the following D days (1\leq i\leq D), the infection spread as follows.

People who were infected at the end of the night of day (i-1) remained infected at the end of the night of day i.
For those who were not infected, they were newly infected if and only if they were living in a room within a distance of X_i from at least one room where an infected person was living at the end of the night of day (i-1). Here, the distance between rooms P and Q is defined as the minimum possible sum of the lengths of the corridors when moving from room P to room Q using only corridors. If it is impossible to move from room P to room Q using only corridors, the distance is set to 10^{100}.

For each i (1\leq i\leq N), print the day on which the person living in room i was newly infected. If they were not infected by the end of the night of day D, print -1.

Constraints

• 1 \leq N\leq 3\times 10^5
• 0 \leq M\leq 3\times 10^5
• 1 \leq U_i < V_i\leq N
• All (U_i,V_i) are different.
• 1\leq W_i\leq 10^9
• 1 \leq K\leq N
• 1\leq A_1<A_2<\cdots<A_K\leq N
• 1 \leq D\leq 3\times 10^5
• 1\leq X_i\leq 10^9
• All input values are integers.

Sample Input 1

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

Sample Output 1

0
1
1
2

The infection spreads as follows.

• On the night of day 0, the person living in room 1 gets infected.
• The distances between room 1 and rooms 2,3,4 are 2,3,5, respectively. Thus, since X_1=3, the people living in rooms 2 and 3 are newly infected on the night of day 1.
• The distance between rooms 3 and 4 is 2. Thus, since X_2=3, the person living in room 4 also gets infected on the night of day 2.

Therefore, the people living in rooms 1,2,3,4 were newly infected on days 0,1,1,2, respectively, so print 0,1,1,2 in this order on separate lines.

Sample Input 2

7 7
1 2 2
2 3 3
3 4 1
4 5 1
5 6 3
3 7 1
4 7 1
2
1 6
2
2 3

Sample Output 2

0
1
2
-1
2
0
-1

Sample Input 3

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

Sample Output 3

0
2
0
-1
-1

Note that it is not always possible to move between any two rooms using only corridors.