Problem Statement

You are given a string S consisting of v and w.

Print the number of "bottoms" in the string S (see the figure at Sample Input/Output).

Constraints

• S is a string consisting of v and w.
• The length of S is between 1 and 100, inclusive.

Sample Input 1

vvwvw

Sample Output 1

7

The image above shows the seven "bottoms" in the string vvwvw.

Sample Input 2

v

Sample Output 2

1

Sample Input 3

wwwvvvvvv

Sample Output 3

12

Problem Statement

In the figure shown in the image below, are the points numbered a and b directly connected by a line segment?

Constraints

• 1 \leq a \lt b \leq 10
• a and b are integers.

Sample Input 1

4 5

Sample Output 1

Yes

In the figure shown in the Problem Statement, the points numbered 4 and 5 are directly connected by a line segment.
Thus, Yes should be printed.

Sample Input 2

3 5

Sample Output 2

No

In the figure shown in the Problem Statement, the points numbered 3 and 5 are not directly connected by a line segment.
Thus, No should be printed.

Sample Input 3

1 10

Sample Output 3

Yes

Problem Statement

You are given an H-by-W matrix A.
The element at the i-th row from the top and j-th column from the left of A is A_{i,j}.

Let B be a W-by-H matrix whose element at the i-th row from the top and j-th column from the left equals A_{j, i}.
That is, B is the transpose of A.

Print B.

Constraints

• 1\leq H,W \leq 10^5
• H \times W \leq 10^5
• 1 \leq A_{i,j} \leq 10^9
• All values in input are integers.

Sample Input 1

4 3
1 2 3
4 5 6
7 8 9
10 11 12

Sample Output 1

1 4 7 10
2 5 8 11
3 6 9 12

For example, we have A_{2,1}=4, so the element at the 1-st row from the top and 2-nd column from the left of the transpose B is 4.

Sample Input 2

2 2
1000000000 1000000000
1000000000 1000000000

Sample Output 2

1000000000 1000000000
1000000000 1000000000

Problem Statement

Naohiro had N+1 consecutive integers, one of each, but he lost one of them.

The remaining N integers are given in arbitrary order as A_1,\ldots,A_N. Find the lost integer.

The given input guarantees that the lost integer is uniquely determined.

Constraints

• 2 \leq N \leq 100
• 1 \leq A_i \leq 1000
• All input values are integers.
• The lost integer is uniquely determined.

Sample Input 1

3
2 3 5

Sample Output 1

4

Naohiro originally had four integers, 2,3,4,5, then lost 4, and now has 2,3,5.

Print the lost integer, 4.

Sample Input 2

8
3 1 4 5 9 2 6 8

Sample Output 2

7

Sample Input 3

16
152 153 154 147 148 149 158 159 160 155 156 157 144 145 146 150

Sample Output 3

151

Problem Statement

Takahashi has a red jewel of level N. (He has no other jewels.)
Takahashi can do the following operations any number of times.

• Convert a red jewel of level n (n is at least 2) into "a red jewel of level (n-1) and X blue jewels of level n".
• Convert a blue jewel of level n (n is at least 2) into "a red jewel of level (n-1) and Y blue jewels of level (n-1)".

Takahashi wants as many blue jewels of level 1 as possible. At most, how many blue jewels of level 1 can he obtain by the operations?

Constraints

• 1 \leq N \leq 10
• 1 \leq X \leq 5
• 1 \leq Y \leq 5
• All values in input are integers.

Sample Input 1

2 3 4

Sample Output 1

12

Takahashi can obtain 12 blue jewels of level 1 by the following conversions.

• First, he converts a red jewel of level 2 into a red jewel of level 1 and 3 blue jewels of level 2.
  • After this operation, Takahashi has 1 red jewel of level 1 and 3 blue jewels of level 2.
• Next, he repeats the following conversion 3 times: converting a blue jewel of level 2 into a red jewel of level 1 and 4 blue jewels of level 1.
  • After these operations, Takahashi has 4 red jewels of level 1 and 12 blue jewels of level 1.
• He cannot perform a conversion anymore.

He cannot obtain more than 12 blue jewels of level 1, so the answer is 12.

Sample Input 2

1 5 5

Sample Output 2

0

Takahashi may not be able to obtain a blue jewel of level 1.

Sample Input 3

10 5 5

Sample Output 3

3942349900

Note that the answer may not fit into a 32-bit integer type.

Problem Statement

You are given a non-negative integer N. Print all non-negative integers x that satisfy the following condition in ascending order.

• The set of the digit positions containing 1 in the binary representation of x is a subset of the set of the digit positions containing 1 in the binary representation of N.
  • That is, the following holds for every non-negative integer k: if the digit in the "2^ks" place of x is 1, the digit in the 2^ks place of N is 1.

Constraints

• N is an integer.
• 0 \le N < 2^{60}
• In the binary representation of N, at most 15 digit positions contain 1.

Sample Input 1

11

Sample Output 1

0
1
2
3
8
9
10
11

The binary representation of N = 11_{(10)} is 1011_{(2)}.
The non-negative integers x that satisfy the condition are:

• 0000_{(2)}=0_{(10)}
• 0001_{(2)}=1_{(10)}
• 0010_{(2)}=2_{(10)}
• 0011_{(2)}=3_{(10)}
• 1000_{(2)}=8_{(10)}
• 1001_{(2)}=9_{(10)}
• 1010_{(2)}=10_{(10)}
• 1011_{(2)}=11_{(10)}

Sample Input 2

0

Sample Output 2

0

Sample Input 3

576461302059761664

Sample Output 3

0
524288
549755813888
549756338176
576460752303423488
576460752303947776
576461302059237376
576461302059761664

The input may not fit into a 32-bit signed integer.

Problem Statement

You are given a tree with N vertices: vertex 1, vertex 2, \ldots, vertex N. The i-th edge (1\leq i\lt N) connects vertex u _ i and vertex v _ i.

Consider repeating the following operation some number of times:

• Choose one leaf vertex v and delete it along with all incident edges.

Find the minimum number of operations required to delete vertex 1.

Constraints

• 2\leq N\leq3\times10^5
• 1\leq u _ i\lt v _ i\leq N\ (1\leq i\lt N)
• The given graph is a tree.
• All input values are integers.

Sample Input 1

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

Sample Output 1

5

The given graph looks like this:

For example, you can choose vertices 9,8,7,6,1 in this order to delete vertex 1 in five operations.

Vertex 1 cannot be deleted in four or fewer operations, so print 5.

Sample Input 2

6
1 2
2 3
2 4
3 5
3 6

Sample Output 2

1

In the given graph, vertex 1 is a leaf. Hence, you can choose and delete vertex 1 in the first operation.

Sample Input 3

24
3 6
7 17
7 20
7 11
14 18
17 21
6 19
5 22
9 24
11 14
6 23
8 17
9 12
4 17
2 15
1 17
3 9
10 16
7 13
2 16
1 16
5 7
1 3

Sample Output 3

12

Problem Statement

Given is a string S consisting of K, E, Y.

How many strings are there that can be obtained with at most K swaps of two adjacent characters in S?

Constraints

• 2 \leq |S| \leq 30
• 0 \leq K \leq 10^9
• S consists of K, E, Y.

Sample Input 1

KEY
1

Sample Output 1

3

With at most one swap, there are three strings that can be obtained: KEY, EKY, KYE.

Sample Input 2

KKEE
2

Sample Output 2

4

With at most two swaps, there are four strings that can be obtained: KKEE, KEKE, EKKE, KEEK.

Sample Input 3

KKEEYY
1000000000

Sample Output 3

90

Problem Statement

On a blackboard, there are N sets S_1,S_2,\dots,S_N consisting of integers between 1 and M. Here, S_i = \lbrace S_{i,1},S_{i,2},\dots,S_{i,A_i} \rbrace.

You may perform the following operation any number of times (possibly zero):

• choose two sets X and Y with at least one common element. Erase them from the blackboard, and write X\cup Y on the blackboard instead.

Here, X\cup Y denotes the set consisting of the elements contained in at least one of X and Y.

Determine if one can obtain a set containing both 1 and M. If it is possible, find the minimum number of operations required to obtain it.

Constraints

• 1 \le N \le 2 \times 10^5
• 2 \le M \le 2 \times 10^5
• 1 \le \sum_{i=1}^{N} A_i \le 5 \times 10^5
• 1 \le S_{i,j} \le M(1 \le i \le N,1 \le j \le A_i)
• S_{i,j} \neq S_{i,k}(1 \le j < k \le A_i)
• All values in the input are integers.

Sample Input 1

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

Sample Output 1

2

First, choose and remove \lbrace 1,2 \rbrace and \lbrace 2,3 \rbrace to obtain \lbrace 1,2,3 \rbrace.

Then, choose and remove \lbrace 1,2,3 \rbrace and \lbrace 3,4,5 \rbrace to obtain \lbrace 1,2,3,4,5 \rbrace.

Thus, one can obtain a set containing both 1 and M with two operations. Since one cannot achieve the objective by performing the operation only once, the answer is 2.

Sample Input 2

1 2
2
1 2

Sample Output 2

0

S_1 already contains both 1 and M, so the minimum number of operations required is 0.

Sample Input 3

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

Sample Output 3

-1

Sample Input 4

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

Sample Output 4

2