Problem Statement

There is an enemy with stamina A. Every time you attack the enemy, its stamina reduces by B.

At least how many times do you need to attack the enemy to make its stamina 0 or less?

Constraints

• 1 \le A,B \le 10^{18}
• A and B are integers.

Sample Input 1

7 3

Sample Output 1

3

Attacking three times make the enemy's stamina -2.

Attacking only twice makes the stamina 1, so you need to attack it three times.

Sample Input 2

123456789123456789 987654321

Sample Output 2

124999999

Sample Input 3

999999999999999998 2

Sample Output 3

499999999999999999

Problem Statement

You are given a string S, which represents a weather forecast for the seven days starting tomorrow.
The i-th of those seven days is forecast to be sunny if the i-th character of S is o, and rainy if that character is x.

Tell us whether the N-th day is forecast to be sunny.

Constraints

• N is an integer between 1 and 7 (inclusive).
• S is a string of length 7 consisting of o and x.

Sample Input 1

4
oooxoox

Sample Output 1

No

The forecast for each of the seven days starting tomorrow is as follows: sunny, sunny, sunny, rainy, sunny, sunny, rainy.
In particular, the fourth day is forecast to be rainy.

Sample Input 2

7
ooooooo

Sample Output 2

Yes

Problem Statement

You are given positive integers A and B.
Let us calculate A+B (in decimal). If it does not involve a carry, print Easy; if it does, print Hard.

Constraints

• A and B are integers.
• 1 \le A,B \le 10^{18}

Sample Input 1

229 390

Sample Output 1

Hard

When calculating 229+390, we have a carry from the tens digit to the hundreds digit, so the answer is Hard.

Sample Input 2

123456789 9876543210

Sample Output 2

Easy

We do not have a carry here; the answer is Easy.
Note that the input may not fit into a 32-bit integer.

Problem Statement

There is a keyboard with 26 keys arranged on a number line.

The arrangement of this keyboard is represented by a string S, which is a permutation of ABCDEFGHIJKLMNOPQRSTUVWXYZ. The key corresponding to the character S_x is located at coordinate x (1 \leq x \leq 26). Here, S_x denotes the x-th character of S.

You will use this keyboard to input ABCDEFGHIJKLMNOPQRSTUVWXYZ in this order, typing each letter exactly once with your right index finger. To input a character, you need to move your finger to the coordinate of the key corresponding to that character and press the key.

Initially, your finger is at the coordinate of the key corresponding to A. Find the minimal possible total traveled distance of your finger from pressing the key for A to pressing the key for Z. Here, pressing a key does not contribute to the distance.

Constraints

• S is a permutation of ABCDEFGHIJKLMNOPQRSTUVWXYZ.

Sample Input 1

ABCDEFGHIJKLMNOPQRSTUVWXYZ

Sample Output 1

25

From pressing the key for A to pressing the key for Z, you need to move your finger 1 unit at a time in the positive direction, resulting in a total traveled distance of 25. It is impossible to press all keys with a total traveled distance less than 25, so print 25.

Sample Input 2

MGJYIZDKSBHPVENFLQURTCWOAX

Sample Output 2

223

Problem Statement

Print all strictly increasing integer sequences of length N where all elements are between 1 and M (inclusive), in lexicographically ascending order.

Notes

For two integer sequences of the same length A_1,A_2,\dots,A_N and B_1,B_2,\dots,B_N, A is said to be lexicographically earlier than B if and only if:

• there is an integer i (1 \le i \le N) such that A_j=B_j for all integers j satisfying 1 \le j < i, and A_i < B_i.

An integer sequence A_1,A_2,\dots,A_N is said to be strictly increasing if and only if:

• A_i < A_{i+1} for all integers i (1 \le i \le N-1).

Constraints

• 1 \le N \le M \le 10
• All values in input are integers.

Sample Input 1

2 3

Sample Output 1

1 2 
1 3 
2 3 

The sought sequences are (1,2),(1,3),(2,3), which should be printed in lexicographically ascending order.

Sample Input 2

3 5

Sample Output 2

1 2 3 
1 2 4 
1 2 5 
1 3 4 
1 3 5 
1 4 5 
2 3 4 
2 3 5 
2 4 5 
3 4 5 

Problem Statement

You are given strings S and T consisting of uppercase English letters.

You may perform the following two types of operations any number of times (possibly zero) in any order:

• Insert one character A at any position in S (possibly the beginning or the end).
• Choose one character A in S and delete it. The remaining characters are concatenated in their original order.

Determine whether it is possible to make S equal to T, and if so, find the minimum total number of operations required.

Constraints

• S and T are strings of uppercase English letters with length between 1 and 3\times 10^5, inclusive.

Sample Input 1

ABC
BACA

Sample Output 1

3

It is possible to make S equal to T in three operations in total, as follows:

• Insert one A between the second and third characters of S. Now, S= ABAC.
• Delete the first character of S, which is A. Now, S= BAC.
• Insert one A at the end of S. Now, S= BACA.

It is impossible to make S equal to T in two or fewer operations, so the answer is 3.

Sample Input 2

ABC
ARC

Sample Output 2

-1

No matter how operations are performed, it is impossible to make S equal to T.

Sample Input 3

ABC
ABC

Sample Output 3

0

No operations need to be performed.

Sample Input 4

AAAWAZAAAABAAAU
AWAAZABAAAAAUA

Sample Output 4

9

Problem Statement

You are given a sequence of positive integers A=(a_1,\ldots,a_N) of length N.
There are (2^N-1) ways to choose one or more terms of A. How many of them have an integer-valued average? Find the count modulo 998244353.

Constraints

• 1 \leq N \leq 100
• 1 \leq a_i \leq 10^9
• All values in input are integers.

Sample Input 1

3
2 6 2

Sample Output 1

6

For each way to choose terms of A, the average is obtained as follows:

• If just a_1 is chosen, the average is \frac{a_1}{1}=\frac{2}{1} = 2, which is an integer.

• If just a_2 is chosen, the average is \frac{a_2}{1}=\frac{6}{1} = 6, which is an integer.

• If just a_3 is chosen, the average is \frac{a_3}{1}=\frac{2}{1} = 2, which is an integer.

• If a_1 and a_2 are chosen, the average is \frac{a_1+a_2}{2}=\frac{2+6}{2} = 4, which is an integer.

• If a_1 and a_3 are chosen, the average is \frac{a_1+a_3}{2}=\frac{2+2}{2} = 2, which is an integer.

• If a_2 and a_3 are chosen, the average is \frac{a_2+a_3}{2}=\frac{6+2}{2} = 4, which is an integer.

• If a_1, a_2, and a_3 are chosen, the average is \frac{a_1+a_2+a_3}{3}=\frac{2+6+2}{3} = \frac{10}{3}, which is not an integer.

Therefore, 6 ways satisfy the condition.

Sample Input 2

5
5 5 5 5 5

Sample Output 2

31

Regardless of the choice of one or more terms of A, the average equals 5.

Problem Statement

You are given a string S of length N consisting of three kinds of characters: A, B, and C.

There are \dfrac{N(N+1)}2 non-empty contiguous substrings of S. Find how many of them contain more As than Bs.

Note that two substrings are counted separately if they are taken from different positions in S, even if they are equal as strings.

Constraints

• 1\le N\le5\times10 ^ 5
• S is a string of length N consisting of A, B, and C.
• N is an integer.

Sample Input 1

10
ACBBCABCAB

Sample Output 1

8

The following eight substrings satisfy the condition:

• A: 1st to 1st character of S
• AC: 1st to 2nd character of S
• CA: 5th to 6th character of S
• CABCA: 5th to 9th character of S
• A: 6th to 6th character of S
• ABCA: 6th to 9th character of S
• CA: 8th to 9th character of S
• A: 9th to 9th character of S

All other substrings do not satisfy the condition, so print 8.

Note that A and CA can be taken from multiple positions, but they are counted separately if taken from different positions.

Sample Input 2

4
CCBC

Sample Output 2

0

There may be no substrings that satisfy the condition.

Sample Input 3

36
CABACBBBBBAABABACCBCABCCABAABABBCBAC

Sample Output 3

136

Problem Statement

There are N buildings, building 1, building 2, \ldots, building N, arranged in this order in a straight line from west to east. Building 1 is the westernmost, and building N is the easternmost. The height of building i\ (1\leq i\leq N) is H_i.

For a pair of integers (i,j)\ (1\leq i\lt j\leq N), building j can be seen from building i if the following condition is satisfied.

• There is no building taller than building j between buildings i and j. In other words, there is no integer k\ (i\lt k\lt j) such that H_k > H_j.

You are given Q queries. In the i-th query, given a pair of integers (l_i,r_i)\ (l_i\lt r_i), find the number of buildings to the east of building r_i (that is, buildings r_i + 1, r_i + 2, \ldots, N) that can be seen from both buildings l_i and r_i.

Constraints

• 2 \leq N \leq 2 \times 10^5
• 1 \leq Q \leq 2 \times 10^5
• 1 \leq H_i \leq N
• H_i\neq H_j\ (i\neq j)
• 1 \leq l_i < r_i \leq N
• All input values are integers.

Sample Input 1

5 3
2 1 4 3 5
1 2
3 5
1 4

Sample Output 1

2
0
1

• For the first query, among the buildings to the east of building 2, buildings 3 and 5 can be seen from both buildings 1 and 2, so the answer is 2.
• For the second query, there are no buildings to the east of building 5.
• For the third query, among the buildings to the east of building 4, building 5 can be seen from both buildings 1 and 4, so the answer is 1.

Sample Input 2

10 10
2 1 5 3 4 6 9 8 7 10
3 9
2 5
4 8
5 6
3 8
2 10
7 8
6 7
8 10
4 10

Sample Output 2

1
3
1
2
1
0
1
1
0
0