Problem Statement

You are given three integers A, B and C.

Determine if there exists an equilateral triangle whose sides have lengths A, B and C.

Constraints

• All values in input are integers.
• 1 \leq A,B,C \leq 100

Sample Input 1

2 2 2

Sample Output 1

Yes

• There exists an equilateral triangle whose sides have lengths 2, 2 and 2.

Sample Input 2

3 4 5

Sample Output 2

No

• There is no equilateral triangle whose sides have lengths 3, 4 and 5.

Problem Statement

There are N people numbered 1 to N. Each person wears a red hat or a blue hat.

You are given a string s representing the colors of the people. Person i wears a red hat if s_i is R, and a blue hat if s_i is B.

Determine if there are more people wearing a red hat than people wearing a blue hat.

Constraints

• 1 \leq N \leq 100
• |s| = N
• s_i is R or B.

Sample Input 1

4
RRBR

Sample Output 1

Yes

• There are three people wearing a red hat, and one person wearing a blue hat.
• Since there are more people wearing a red hat than people wearing a blue hat, the answer is Yes.

Sample Input 2

4
BRBR

Sample Output 2

No

• There are two people wearing a red hat, and two people wearing a blue hat.
• Since there are as many people wearing a red hat as people wearing a blue hat, the answer is No.

Problem Statement

There are N squares numbered 1 to N from left to right. Each square has a character written on it, and Square i has a letter s_i. Besides, there is initially one golem on each square.

Snuke cast Q spells to move the golems.

The i-th spell consisted of two characters t_i and d_i, where d_i is L or R. When Snuke cast this spell, for each square with the character t_i, all golems on that square moved to the square adjacent to the left if d_i is L, and moved to the square adjacent to the right if d_i is R.

However, when a golem tried to move left from Square 1 or move right from Square N, it disappeared.

Find the number of golems remaining after Snuke cast the Q spells.

Constraints

• 1 \leq N,Q \leq 2 \times 10^{5}
• |s| = N
• s_i and t_i are uppercase English letters.
• d_i is L or R.

Sample Input 1

3 4
ABC
A L
B L
B R
A R

Sample Output 1

2

• Initially, there is one golem on each square.
• In the first spell, the golem on Square 1 tries to move left and disappears.
• In the second spell, the golem on Square 2 moves left.
• In the third spell, no golem moves.
• In the fourth spell, the golem on Square 1 moves right.
• After the four spells are cast, there is one golem on Square 2 and one golem on Square 3, for a total of two golems remaining.

Sample Input 2

8 3
AABCBDBA
A L
B R
A R

Sample Output 2

5

• After the three spells are cast, there is one golem on Square 2, two golems on Square 4 and two golems on Square 6, for a total of five golems remaining.
• Note that a single spell may move multiple golems.

Sample Input 3

10 15
SNCZWRCEWB
B R
R R
E R
W R
Z L
S R
Q L
W L
B R
C L
A L
N L
E R
Z L
S L

Sample Output 3

3

Problem Statement

Snuke has a blackboard and a set S consisting of N integers. The i-th element in S is S_i.

He wrote an integer X on the blackboard, then performed the following operation N times:

• Choose one element from S and remove it.
• Let x be the number written on the blackboard now, and y be the integer removed from S. Replace the number on the blackboard with x \bmod {y}.

There are N! possible orders in which the elements are removed from S. For each of them, find the number that would be written on the blackboard after the N operations, and compute the sum of all those N! numbers modulo 10^{9}+7.

Constraints

• All values in input are integers.
• 1 \leq N \leq 200
• 1 \leq S_i, X \leq 10^{5}
• S_i are pairwise distinct.

Sample Input 1

2 19
3 7

Sample Output 1

3

• There are two possible orders in which we remove the numbers from S.
• If we remove 3 and 7 in this order, the number on the blackboard changes as follows: 19 \rightarrow 1 \rightarrow 1.
• If we remove 7 and 3 in this order, the number on the blackboard changes as follows: 19 \rightarrow 5 \rightarrow 2.
• The output should be the sum of these: 3.

Sample Input 2

5 82
22 11 6 5 13

Sample Output 2

288

Sample Input 3

10 100000
50000 50001 50002 50003 50004 50005 50006 50007 50008 50009

Sample Output 3

279669259

• Be sure to compute the sum modulo 10^{9}+7.

Problem Statement

Today, Snuke will eat B pieces of black chocolate and W pieces of white chocolate for an afternoon snack.

He will repeat the following procedure until there is no piece left:

• Choose black or white with equal probability, and eat a piece of that color if it exists.

For each integer i from 1 to B+W (inclusive), find the probability that the color of the i-th piece to be eaten is black. It can be shown that these probabilities are rational, and we ask you to print them modulo 10^9 + 7, as described in Notes.

Notes

When you print a rational number, first write it as a fraction \frac{y}{x}, where x, y are integers and x is not divisible by 10^9 + 7 (under the constraints of the problem, such representation is always possible). Then, you need to print the only integer z between 0 and 10^9 + 6, inclusive, that satisfies xz \equiv y \pmod{10^9 + 7}.

Constraints

• All values in input are integers.
• 1 \leq B,W \leq 10^{5}

Sample Input 1

2 1

Sample Output 1

500000004
750000006
750000006

• There are three possible orders in which Snuke eats the pieces:
  • white, black, black
  • black, white, black
  • black, black, white
• with probabilities \frac{1}{2}, \frac{1}{4}, \frac{1}{4}, respectively. Thus, the probabilities of eating a black piece first, second and third are \frac{1}{2},\frac{3}{4} and \frac{3}{4}, respectively.

Sample Input 2

3 2

Sample Output 2

500000004
500000004
625000005
187500002
187500002

• They are \frac{1}{2},\frac{1}{2},\frac{5}{8},\frac{11}{16} and \frac{11}{16}, respectively.

Sample Input 3

6 9

Sample Output 3

500000004
500000004
500000004
500000004
500000004
500000004
929687507
218750002
224609377
303710940
633300786
694091802
172485353
411682132
411682132

Problem Statement

In Takaha-shi, the capital of Republic of AtCoder, there are N roads extending east and west, and M roads extending north and south. There are no other roads. The i-th east-west road from the north and the j-th north-south road from the west cross at the intersection (i, j). Two east-west roads do not cross, nor do two north-south roads. The distance between two adjacent roads in the same direction is 1.

Each road is one-way; one can only walk in one direction. The permitted direction for each road is described by a string S of length N and a string T of length M, as follows:

• If the i-th character in S is W, one can only walk westward along the i-th east-west road from the north;
• If the i-th character in S is E, one can only walk eastward along the i-th east-west road from the north;
• If the i-th character in T is N, one can only walk northward along the i-th north-south road from the west;
• If the i-th character in T is S, one can only walk southward along the i-th south-west road from the west.

Process the following Q queries:

• In the i-th query, a_i, b_i, c_i and d_i are given. What is the minimum distance to travel to reach the intersection (c_i, d_i) from the intersection (a_i, b_i) by walking along the roads?

Constraints

• 2 \leq N \leq 100000
• 2 \leq M \leq 100000
• 2 \leq Q \leq 200000
• |S| = N
• S consists of W and E.
• |T| = M
• T consists of N and S.
• 1 \leq a_i \leq N
• 1 \leq b_i \leq M
• 1 \leq c_i \leq N
• 1 \leq d_i \leq M
• (a_i, b_i) \neq (c_i, d_i)

Sample Input 1

4 5 4
EEWW
NSNNS
4 1 1 4
1 3 1 2
4 2 3 2
3 3 3 5

Sample Output 1

6
11
5
4

The permitted direction for each road is shown in the following figure (north upward):

For each of the four queries, a route that achieves the minimum travel distance is as follows:

Sample Input 2

3 3 2
EEE
SSS
1 1 3 3
3 3 1 1

Sample Output 2

4
-1

The travel may be impossible.

Sample Input 3

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

Sample Output 3

9
-1
4
9
2
3
7
7
6
-1