Problem Statement

There are N boxes numbered 1 to N and N items numbered 1 to N. Item i (1 \leq i \leq N) is in box A_i and has a weight of W_i.

You can repeatedly perform the operation of choosing an item and moving it to another box zero or more times. If the weight of the item being moved is w, the cost of the operation is w.

Find the minimum total cost required to make each box contain exactly one item.

Constraints

• 1 \leq N \leq 10^{5}
• 1 \leq A_i \leq N (1 \leq i \leq N)
• 1 \leq W_i \leq 10^{4} (1 \leq i \leq N)
• All input values are integers.

Sample Input 1

5
2 2 3 3 5
33 40 2 12 16

Sample Output 1

35

With the following two moves, you can make each box contain exactly one item:

• Move item 1 from box 2 to box 1. The cost is 33.
• Move item 3 from box 3 to box 4. The cost is 2.

The total cost of these two moves is 35. It is impossible to make each box contain exactly one item with a cost less than 35, so print 35.

Sample Input 2

12
3 6 7 4 12 4 8 11 11 1 8 11
3925 9785 9752 3587 4013 1117 3937 7045 6437 6208 3391 6309

Sample Output 2

17254

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

There is a grid with 10^9 by 10^9 squares. Let (i, j) denote the square at the (i + 1)-th row from the top and the (j + 1)-th column from the left (0 \leq i, j \lt 10^9). (Note the unusual index assignment.)
Each square is black or white. The color of the square (i, j) is represented by a character P[i \bmod N][j \bmod N], where B means black, and W means white. Here, a \bmod b denotes the remainder when a is divided by b.

Answer Q queries.
Each query gives you four integers A, B, C, D and asks you to find the number of black squares contained in the rectangular area with (A, B) as the top-left corner and (C, D) as the bottom-right corner.

Constraints

• 1 \leq N \leq 1000
• P[i][j] is W or B.
• 1 \leq Q \leq 2 \times 10^5
• 0 \leq A \leq C \lt 10^9
• 0 \leq B \leq D \lt 10^9
• N, Q, A, B, C, D are all integers.

Sample Input 1

3 2
WWB
BBW
WBW
1 2 3 4
0 3 4 5

Sample Output 1

4
7

The figure below illustrates the upper left part of the grid.

For the first query, the rectangular area with (1, 2) as the top-left corner and (3, 4) as the bottom-right corner, surrounded by the red frame in the figure, contains four black squares.
For the second query, the rectangular area with (0, 3) as the top-left corner and (4, 5) as the bottom-right corner, surrounded by the blue frame in the figure, contains seven black squares.

Sample Input 2

10 5
BBBWWWBBBW
WWWWWBBBWB
BBBWBBWBBB
BBBWWBWWWW
WWWWBWBWBW
WBBWBWBBBB
WWBBBWWBWB
WBWBWWBBBB
WBWBWBBWWW
WWWBWWBWWB
5 21 21 93
35 35 70 43
55 72 61 84
36 33 46 95
0 0 999999999 999999999

Sample Output 2

621
167
44
344
500000000000000000

Problem Statement

You are given a simple undirected graph with N vertices and M edges. The vertices are numbered 1, \dots, N, and the i-th (1 \leq i \leq M) edge connects Vertices U_i and V_i.

There are 2^N ways to paint each vertex red or blue. Find the number, modulo 998244353, of such ways that satisfy all of the following conditions:

• There are exactly K vertices painted red.
• There is an even number of edges connecting vertices painted in different colors.

Constraints

• 2 \leq N \leq 2 \times 10^5
• 1 \leq M \leq 2 \times 10^5
• 0 \leq K \leq N
• 1 \leq U_i \lt V_i \leq N \, (1 \leq i \leq M)
• (U_i, V_i) \neq (U_j, V_j) \, (i \neq j)
• All values in input are integers.

Sample Input 1

4 4 2
1 2
1 3
2 3
3 4

Sample Output 1

2

The following two ways satisfy the conditions.

• Paint Vertices 1 and 2 red and Vertices 3 and 4 blue.
• Paint Vertices 3 and 4 red and Vertices 1 and 2 blue.

In either of the ways above, the 2-nd and 3-rd edges connect vertices painted in different colors.

Sample Input 2

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

Sample Output 2

64

Problem Statement

A monster with health H has appeared in front of you, and a turn-based battle has started.

In each turn 1,2,…, you cast one of N spells, spells 1,…,N.

If you cast spell i in turn j, the monster's health reduces by d_i in each turn j,j+1,…,j+t_i －1.

Find the earliest turn that you can make the monster's health 0 or less.

Constraints

• 1 \leq N \leq 3 \times 10^5
• 1 \leq H \leq 10^{18}
• 1 \leq t_i,d_i \leq 10^9
• All values in the input are integers.

Sample Input 1

2 20
2 2
5 1

Sample Output 1

6

The following procedure makes the monster's health 0 or less in turn 6, which is the earliest.

• Cast spell 1 in turn 1. Due to the spell cast in turn 1, the monster's health reduces by 2 and becomes 18.
• Cast spell 2 in turn 2. Due to the spells cast in turns 1 and 2, the monster's health reduces by 2+1=3 and becomes 15.
• Cast spell 1 in turn 3. Due to the spells cast in turns 2 and 3, the monster's health reduces by 1+2=3 and becomes 12.
• Cast spell 2 in turn 4. Due to the spells cast in turns 2,3 and 4, the monster's health reduces by 1+2+1=4 and becomes 8.
• Cast spell 1 in turn 5. Due to the spells cast in turns 2,4 and 5, the monster's health reduces by 1+1+2=4 and becomes 4.
• Cast spell 2 in turn 6. Due to the spells cast in turns 2,4,5 and 6, the monster's health reduces by 1+1+2+1=5 and becomes -1.

Sample Input 2

10 200
1 21
1 1
1 1
8 4
30 1
3 1
10 2
8 1
9 1
4 4

Sample Output 2

9