Problem Statement

Takahashi wants to send a letter to Santa Claus. He has an envelope with an X-yen (Japanese currency) stamp stuck on it.
To be delivered to Santa Claus, the envelope must have stamps in a total value of at least Y yen.
Takahashi will put some more 10-yen stamps so that the envelope will have stamps worth at least Y yen in total.
At least how many more 10-yen stamps does Takahashi need to put on the envelope?

Constraints

• X and Y are integers.
• 1 \le X,Y \le 1000

Sample Input 1

80 94

Sample Output 1

2

• After adding zero 10-yen stamps to the 80-yen stamp, the total is 80 yen, which is less than the required amount of 94 yen.
• After adding one 10-yen stamp to the 80-yen stamp, the total is 90 yen, which is less than the required amount of 94 yen.
• After adding two 10-yen stamps to the 80-yen stamp, the total is 100 yen, which is not less than the required amount of 94 yen.

Sample Input 2

1000 63

Sample Output 2

0

The envelope may already have a stamp with enough value.

Sample Input 3

270 750

Sample Output 3

48

Problem Statement

Given integers A and B, find A+B.
This is a N-choice problem; the i-th choice is C_i.
Print the index of the correct choice.

Constraints

• All values in the input are integers.
• 1 \le N \le 300
• 1 \le A,B \le 1000
• 1 \le C_i \le 2000
• C_i are pairwise distinct. In other words, no two choices have the same value.
• There is exactly one i such that A+B=C_i. In other words, there is always a unique correct choice.

Sample Input 1

3 125 175
200 300 400

Sample Output 1

2

We have 125+175 = 300.
The first, second, and third choices are 200, 300, and 400, respectively.
Thus, the 2-nd choice is correct, so 2 should be printed.

Sample Input 2

1 1 1
2

Sample Output 2

1

The problem may be a one-choice problem.

Sample Input 3

5 123 456
135 246 357 468 579

Sample Output 3

5

Problem Statement

Let us call a string consisting of uppercase and lowercase English alphabets a wonderful string if all of the following conditions are satisfied:

• The string contains an uppercase English alphabet.
• The string contains a lowercase English alphabet.
• All characters in the string are pairwise distinct.

For example, AtCoder and Aa are wonderful strings, while atcoder and Perfect are not.

Given a string S, determine if S is a wonderful string.

Constraints

• 1 \le |S| \le 100
• S is a string consisting of uppercase and lowercase English alphabets.

Sample Input 1

AtCoder

Sample Output 1

Yes

AtCoder is a wonderful string because it contains an uppercase English alphabet, a lowercase English alphabet, and all characters in the string are pairwise distinct.

Sample Input 2

Aa

Sample Output 2

Yes

Note that A and a are different characters. This string is a wonderful string.

Sample Input 3

atcoder

Sample Output 3

No

It is not a wonderful string because it does not contain an uppercase English alphabet.

Sample Input 4

Perfect

Sample Output 4

No

It is not a wonderful string because the 2-nd and the 5-th characters are the same.

Problem Statement

Takahashi is exploring a cave in a video game.

The cave consists of N rooms arranged in a row. The rooms are numbered Room 1,2,\ldots,N from the entrance.

Takahashi is initially in Room 1, and the time limit is T.
For each 1 \leq i \leq N-1, he may consume a time of A_i to move from Room i to Room (i+1). There is no other way to move between rooms. He cannot make a move that makes the time limit 0 or less.

There are M bonus rooms in the cave. The i-th bonus room is Room X_i; when he arrives at the room, the time limit increases by Y_i.

Can Takahashi reach Room N?

Constraints

• 2 \leq N \leq 10^5
• 0 \leq M \leq N-2
• 1 \leq T \leq 10^9
• 1 \leq A_i \leq 10^9
• 1 < X_1 < \ldots < X_M < N
• 1 \leq Y_i \leq 10^9
• All values in input are integers.

Sample Input 1

4 1 10
5 7 5
2 10

Sample Output 1

Yes

• Takahashi is initially in Room 1, and the time limit is 10.
• He consumes a time of 5 to move to Room 2. Now the time limit is 5. Then, the time limit increases by 10; it is now 15.
• He consumes a time of 7 to move to Room 3. Now the time limit is 8.
• He consumes a time of 5 to move to Room 4. Now the time limit is 3.

Sample Input 2

4 1 10
10 7 5
2 10

Sample Output 2

No

He cannot move from Room 1 to Room 2.

Problem Statement

You are given strings S and T. S consists of lowercase English letters, and T is obtained by inserting a lowercase English letter into S.

Find the position of the inserted character in T.
If there are multiple candidates, find any of them.

Constraints

• 1 \leq |S| \leq 5\times 10^5
• S consists of lowercase English letters.
• T is obtained by inserting a lowercase English letter into S.

Sample Input 1

atcoder
atcorder

Sample Output 1

5

The 5-th character from the beginning of T, r, is inserted.

Sample Input 2

million
milllion

Sample Output 2

5

One of the 3-rd, 4-th, and 5-th characters from the beginning of T is inserted. Thus, printing any one of 3, 4, and 5 is accepted.

Sample Input 3

vvwvw
vvvwvw

Sample Output 3

3

Problem Statement

We have an empty box.
Takahashi can cast the following two spells any number of times in any order.

• Spell A: puts one new ball into the box.
• Spell B: doubles the number of balls in the box.

Tell us a way to have exactly N balls in the box with at most \mathbf{120} casts of spells.
It can be proved that there always exists such a way under the Constraints given.

There is no way other than spells to alter the number of balls in the box.

Constraints

• 1 \leq N \leq 10^{18}
• All values in input are integers.

Sample Input 1

5

Sample Output 1

AABA

This changes the number of balls as follows: 0 \xrightarrow{A} 1\xrightarrow{A} 2 \xrightarrow{B}4\xrightarrow{A} 5.
There are also other acceptable outputs, such as AAAAA.

Sample Input 2

14

Sample Output 2

BBABBAAAB

This changes the number of balls as follows: 0 \xrightarrow{B} 0 \xrightarrow{B} 0 \xrightarrow{A}1 \xrightarrow{B} 2 \xrightarrow{B} 4 \xrightarrow{A}5 \xrightarrow{A}6 \xrightarrow{A} 7 \xrightarrow{B}14.
It is not required to minimize the length of S.

Problem Statement

A superman, Takahashi, is about to jump off the roof of a building to help a person in trouble on the ground. Takahashi's planet has a constant value g that represents the strength of gravity, and the time it takes for him to reach the ground after starting to fall is \frac{A}{\sqrt{g}}.

It is now time 0, and g = 1. Takahashi will perform the following operation as many times as he wants (possibly zero).

• Use a superpower to increase the value of g by 1. This takes a time of B.

Then, he will jump off the building. After starting to fall, he cannot change the value of g. Additionally, we only consider the time it takes to perform the operation and fall.

Find the earliest time Takahashi can reach the ground.

Constraints

• 1 \leq A \leq 10^{18}
• 1 \leq B \leq 10^{18}
• All values in the input are integers.

Sample Input 1

10 1

Sample Output 1

7.7735026919

• If he performs the operation zero times, he will reach the ground at time 1\times 0+\frac{10}{\sqrt{1}} = 10.
• If he performs the operation once, he will reach the ground at time 1\times 1+\frac{10}{\sqrt{2}} \fallingdotseq 8.07.
• If he performs the operation twice, he will reach the ground at time 1\times 2+\frac{10}{\sqrt{3}} \fallingdotseq 7.77.
• If he performs the operation three times, he will reach the ground at time 1\times 3+\frac{10}{\sqrt{4}} = 8.

Performing the operation four or more times will only delay the time to reach the ground. Therefore, it is optimal to perform the operation twice before jumping off, and the answer is 2+\frac{10}{\sqrt{3}}.

Sample Input 2

5 10

Sample Output 2

5.0000000000

It is optimal not to perform the operation at all.

Sample Input 3

1000000000000000000 100

Sample Output 3

8772053214538.5976562500

Problem Statement

AtCoder in another world holds 10 types of contests called AAC, ..., AJC. There will be N contests from now on.
The types of these N contests are given to you as a string S: if the i-th character of S is x, the i-th contest will be AxC.
AtCoDeer will choose and participate in one or more contests from the N so that the following condition is satisfied.

• In the sequence of contests he will participate in, the contests of the same type are consecutive.
  • Formally, when AtCoDeer participates in x contests and the i-th of them is of type T_i, for every triple of integers (i,j,k) such that 1 \le i < j < k \le x, T_i=T_j must hold if T_i=T_k.

Find the number of ways for AtCoDeer to choose contests to participate in, modulo 998244353.
Two ways to choose contests are considered different when there is a contest c such that AtCoDeer participates in c in one way but not in the other.

Constraints

• 1 \le N \le 1000
• |S|=N
• S consists of uppercase English letters from A through J.

Sample Input 1

4
BGBH

Sample Output 1

13

For example, participating in the 1-st and 3-rd contests is valid, and so is participating in the 2-nd and 4-th contests.
On the other hand, participating in the 1-st, 2-nd, 3-rd, and 4-th contests is invalid, since the participations in ABCs are not consecutive, violating the condition for the triple (i,j,k)=(1,2,3).
Additionally, it is not allowed to participate in zero contests.
In total, there are 13 valid ways to participate in some contests.

Sample Input 2

100
BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBIEIJEIJIJCGCCFGIEBIHFCGFBFAEJIEJAJJHHEBBBJJJGJJJCCCBAAADCEHIIFEHHBGF

Sample Output 2

330219020

Be sure to find the count modulo 998244353.

Problem Statement

You are given an integer N greater than or equal to 2 and a prime P.
Consider the graph G with 2N vertices and (3N-2) edges shown in the figure below.

More specifically, the edges connect the vertices as follows, where the vertices are labeled as Vertex 1, Vertex 2, \ldots, Vertex 2N, and the edges are labeled as Edge 1, Edge 2, \ldots, Edge (3N-2).

• For each 1\leq i\leq N-1, Edge i connects Vertex i and Vertex i+1.
• For each 1\leq i\leq N-1, Edge (N-1+i) connects Vertex N+i and Vertex N+i+1.
• For each 1\leq i\leq N, Edge (2N-2+i) connects Vertex i and Vertex N+i.

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

Find the number of ways, modulo P, to remove exactly i of the 3N-2 edges of G so that the resulting graph is still connected.

Constraints

• 2 \leq N \leq 3000
• 9\times 10^8 \leq P \leq 10^9
• N is an integer.
• P is a prime.

Sample Input 1

3 998244353

Sample Output 1

7 15

In the case N=3, there are 7 ways, shown below, to remove exactly one edge so that the resulting graph is still connected.

There are 15 ways, shown below, to remove exactly two edges so that the resulting graph is still connected.

Thus, these numbers modulo P=998244353 should be printed: 7 and 15, in this order.

Sample Input 2

16 999999937

Sample Output 2

46 1016 14288 143044 1079816 6349672 29622112 110569766 330377828 784245480 453609503 38603306 44981526 314279703 408855776

Be sure to print the numbers modulo P.