Problem Statement

There are zero or more sensors placed on a grid of H rows and W columns. Let (i, j) denote the square in the i-th row from the top and the j-th column from the left.
Whether each square contains a sensor is given by the strings S_1, S_2, \ldots, S_H, each of length W. (i, j) contains a sensor if and only if the j-th character of S_i is #.
These sensors interact with other sensors in the squares horizontally, vertically, or diagonally adjacent to them and operate as one sensor. Here, a cell (x, y) and a cell (x', y') are said to be horizontally, vertically, or diagonally adjacent if and only if \max(|x-x'|,|y-y'|) = 1.
Note that if sensor A interacts with sensor B and sensor A interacts with sensor C, then sensor B and sensor C also interact.

Considering the interacting sensors as one sensor, find the number of sensors on this grid.

Constraints

• 1 \leq H, W \leq 1000
• H and W are integers.
• S_i is a string of length W where each character is # or ..

Sample Input 1

5 6
.##...
...#..
....##
#.#...
..#...

Sample Output 1

3

When considering the interacting sensors as one sensor, the following three sensors exist:

• The interacting sensors at (1,2),(1,3),(2,4),(3,5),(3,6)
• The sensor at (4,1)
• The interacting sensors at (4,3),(5,3)

Sample Input 2

3 3
#.#
.#.
#.#

Sample Output 2

1

Sample Input 3

4 2
..
..
..
..

Sample Output 3

0

Sample Input 4

5 47
.#..#..#####..#...#..#####..#...#...###...#####
.#.#...#.......#.#...#......##..#..#...#..#....
.##....#####....#....#####..#.#.#..#......#####
.#.#...#........#....#......#..##..#...#..#....
.#..#..#####....#....#####..#...#...###...#####

Sample Output 4

7

Problem Statement

We have a sequence of N numbers: A = (a_1, a_2, \dots, a_N).
Process the Q queries explained below.

• Query i: You are given a pair of integers (x_i, k_i). Let us look at the elements of A one by one from the beginning: a_1, a_2, \dots Which element will be the k_i-th occurrence of the number x_i?
  Print the index of that element, or -1 if there is no such element.

Constraints

• 1 \leq N \leq 2 \times 10^5
• 1 \leq Q \leq 2 \times 10^5
• 0 \leq a_i \leq 10^9 (1 \leq i \leq N)
• 0 \leq x_i \leq 10^9 (1 \leq i \leq Q)
• 1 \leq k_i \leq N (1 \leq i \leq Q)
• All values in input are integers.

Sample Input 1

6 8
1 1 2 3 1 2
1 1
1 2
1 3
1 4
2 1
2 2
2 3
4 1

Sample Output 1

1
2
5
-1
3
6
-1
-1

1 occurs in A at a_1, a_2, a_5. Thus, the answers to Query 1 through 4 are 1, 2, 5, -1 in this order.

Sample Input 2

3 2
0 1000000000 999999999
1000000000 1
123456789 1

Sample Output 2

2
-1

Problem Statement

You are given a sequence of length N: A=(A_1,A_2,\ldots,A_N).
Find the number of triples (i,j,k) that satisfy both of the following conditions.

• 1\leq i \lt j \lt k \leq N
• A_i, A_j, and A_k are distinct.

Constraints

• 3 \leq N \leq 2\times 10^5
• 1 \leq A_i \leq 2\times 10^5
• All values in input are integers.

Sample Input 1

4
3 1 4 1

Sample Output 1

2

The two triples (i,j,k) satisfying the conditions are (1,2,3) and (1,3,4).

Sample Input 2

10
99999 99998 99997 99996 99995 99994 99993 99992 99991 99990

Sample Output 2

120

Sample Input 3

15
3 1 4 1 5 9 2 6 5 3 5 8 9 7 9

Sample Output 3

355

Problem Statement

We have a tree with 2^N-1 vertices.
The vertices are numbered 1 through 2^N-1. For each 1\leq i < 2^{N-1}, the following edges exist:

• an undirected edge connecting Vertex i and Vertex 2i,
• an undirected edge connecting Vertex i and Vertex 2i+1.

There is no other edge.

Let the distance between two vertices be the number of edges in the simple path connecting those two vertices.

Find the number, modulo 998244353, of pairs of vertices (i, j) such that the distance between them is D.

Constraints

• 2 \leq N \leq 10^6
• 1 \leq D \leq 2\times 10^6
• All values in input are integers.

Sample Input 1

3 2

Sample Output 1

14

The following figure describes the given tree.

There are 14 pairs of vertices such that the distance between them is 2: (1,4),(1,5),(1,6),(1,7),(2,3),(3,2),(4,1),(4,5),(5,1),(5,4),(6,1),(6,7),(7,1),(7,6).

Sample Input 2

14142 17320

Sample Output 2

11284501

Problem Statement

The Republic of Atcoder has N towns numbered 1 through N, and M highways numbered 1 through M.
Highway i connects Town A_i and Town B_i bidirectionally.

King Takahashi is going to construct (N-M-1) new highways so that the following two conditions are satisfied:

• One can travel between every pair of towns using some number of highways
• For each i=1,\ldots,N, exactly D_i highways are directly connected to Town i

Determine if there is such a way of construction. If it exists, print one.

Constraints

• 2 \leq N \leq 2\times 10^5
• 0 \leq M \lt N-1
• 1 \leq D_i \leq N-1
• 1\leq A_i \lt B_i \leq N
• If i\neq j, then (A_i, B_i) \neq (A_j,B_j).
• All values in input are integers.

Sample Input 1

6 2
1 2 1 2 2 2
2 3
1 4

Sample Output 1

6 2
5 6
4 5

As in the Sample Output, the conditions can be satisfied by constructing highways connecting Towns 6 and 2, Towns 5 and 6, and Towns 4 and 5, respectively.

Another example to satisfy the conditions is to construct highways connecting Towns 6 and 4, Towns 5 and 6, and Towns 2 and 5, respectively.

Sample Input 2

5 1
1 1 1 1 4
2 3

Sample Output 2

-1

Sample Input 3

4 0
3 3 3 3

Sample Output 3

-1