Problem Statement

There are N bridges in AtCoder Village. The height of the bridge numbered i is H_i (i is an integer between 1 and N).
Every two different bridges in the village have different heights.

Print the number representing the highest bridge in the village.

Constraints

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

Sample Input 1

3
50 80 70

Sample Output 1

2

The village has three bridges.
The first, second, and third bridges have heights of 50, 80, and 70, respectively, so the second bridge is the highest.
Thus, 2 should be printed.

Sample Input 2

1
1000000000

Sample Output 2

1

The village has only one bridge, so the first bridge is the highest.

Sample Input 3

10
22 75 26 45 72 81 47 29 97 2

Sample Output 3

9

The village has ten bridges, and the ninth bridge (with a height of 97) is the highest.

Problem Statement

Takahashi is in a building with 100 floors.

He uses the stairs for moving up two floors or less or moving down three floors or less, and uses the elevator otherwise.

Does he use the stairs to move from floor X to floor Y?

Constraints

• 1 \leq X,Y \leq 100
• X \neq Y
• All input values are integers.

Sample Input 1

1 4

Sample Output 1

No

The move from floor 1 to floor 4 involves going up three floors, so Takahashi uses the elevator.

Sample Input 2

99 96

Sample Output 2

Yes

The move from floor 99 to floor 96 involves going down three floors, so Takahashi uses the stairs.

Sample Input 3

100 1

Sample Output 3

No

Problem Statement

Takahashi has N foods in his house. The i-th food has the tastiness of A_i.
He dislikes K of these foods: for each i=1,2,\ldots,K, he dislikes the B_i-th food.

Out of the foods with the greatest tastiness among the N foods, Takahashi will randomly choose one and eat it.
If he has a chance to eat something he dislikes, print Yes; otherwise, print No.

Constraints

• 1\leq K\leq N\leq 100
• 1\leq A_i\leq 100
• 1\leq B_i\leq N
• All B_i are distinct.
• All values in input are integers.

Sample Input 1

5 3
6 8 10 7 10
2 3 4

Sample Output 1

Yes

Among the five foods, the ones with the greatest tastiness are Food 3 and 5, of which he eats one.
He dislikes Food 2, 3, and 4, one of which he has a chance to eat: Food 3.
Therefore, the answer is Yes.

Sample Input 2

5 2
100 100 100 1 1
5 4

Sample Output 2

No

The foods with the greatest tastiness are Food 1, 2, and 3, none of which he has a chance to eat.

Sample Input 3

2 1
100 1
2

Sample Output 3

No

The food with the greatest tastiness is Food 1, which he has no chance to eat.

Problem Statement

Takahashi has a string S consisting of lowercase English letters.

On this string, he will do the operation below just once.

• First, choose a non-negative integer K.
• Then, shift each character of S to the right by K (see below).

Here,

• a shifted to the right by 1 is b;
• b shifted to the right by 1 is c;
• c shifted to the right by 1 is d;
• \cdots
• y shifted to the right by 1 is z;
• z shifted to the right by 1 is a.

For example, b shifted to the right by 4 is f, and y shifted to the right by 3 is b.

You are given a string T. Determine whether Takahashi can make S equal T by the operation above.

Constraints

• Each of S and T is a string of length between 1 and 10^5 (inclusive) consisting of lowercase English letters.
• The lengths of S and T are equal.

Sample Input 1

abc
ijk

Sample Output 1

Yes

When Takahashi chooses K=8,

• a is shifted to the right by 8 and becomes i,
• b is shifted to the right by 8 and becomes j,
• c is shifted to the right by 8 and becomes k,

and now S and T are equal.
Therefore, he can make S equal T, so Yes should be printed.

Sample Input 2

z
a

Sample Output 2

Yes

Choosing K=1 makes S and T equal.
Note that the letter on the right of z is a.

Sample Input 3

ppq
qqp

Sample Output 3

No

There is no non-negative integer K that he can choose to make S equal T, so No should be printed.

Sample Input 4

atcoder
atcoder

Sample Output 4

Yes

Choosing K=0 makes S and T equal.

Problem Statement

There are N creatures standing in a circle, called Snuke 1, 2, ..., N in counter-clockwise order.

When Snuke i (1 \leq i \leq N) receives a gem at time t, S_i units of time later, it will hand that gem to Snuke i+1 at time t+S_i. Here, Snuke N+1 is Snuke 1.

Additionally, Takahashi will hand a gem to Snuke i at time T_i.

For each i (1 \leq i \leq N), find the time when Snuke i receives a gem for the first time. Assume that it takes a negligible time to hand a gem.

Constraints

• 1 \leq N \leq 200000
• 1 \leq S_i,T_i \leq 10^9
• All values in input are integers.

Sample Input 1

3
4 1 5
3 10 100

Sample Output 1

3
7
8

We will list the three Snuke's and Takahashi's actions up to time 13 in chronological order.

Time 3: Takahashi hands a gem to Snuke 1.

Time 7: Snuke 1 hands a gem to Snuke 2.

Time 8: Snuke 2 hands a gem to Snuke 3.

Time 10: Takahashi hands a gem to Snuke 2.

Time 11: Snuke 2 hands a gem to Snuke 3.

Time 13: Snuke 3 hands a gem to Snuke 1.

After that, they will continue handing gems, though it will be irrelevant to the answer.

Sample Input 2

4
100 100 100 100
1 1 1 1

Sample Output 2

1
1
1
1

Note that the values S_i and T_i may not be distinct.

Sample Input 3

4
1 2 3 4
1 2 4 7

Sample Output 3

1
2
4
7

Note that a Snuke may perform multiple transactions simultaneously. Particularly, a Snuke may receive gems simultaneously from Takahashi and another Snuke.

Sample Input 4

8
84 87 78 16 94 36 87 93
50 22 63 28 91 60 64 27

Sample Output 4

50
22
63
28
44
60
64
27