Problem Statement

You planned a trip using trains and buses. The train fare will be A yen (the currency of Japan) if you buy ordinary tickets along the way, and B yen if you buy an unlimited ticket. Similarly, the bus fare will be C yen if you buy ordinary tickets along the way, and D yen if you buy an unlimited ticket.

Find the minimum total fare when the optimal choices are made for trains and buses.

Constraints

• 1 \leq A \leq 1 000
• 1 \leq B \leq 1 000
• 1 \leq C \leq 1 000
• 1 \leq D \leq 1 000
• All input values are integers.

Sample Input 1

600
300
220
420

Sample Output 1

520

The train fare will be 600 yen if you buy ordinary tickets, and 300 yen if you buy an unlimited ticket. Thus, the optimal choice for trains is to buy an unlimited ticket for 300 yen. On the other hand, the optimal choice for buses is to buy ordinary tickets for 220 yen.

Therefore, the minimum total fare is 300 + 220 = 520 yen.

Sample Input 2

555
555
400
200

Sample Output 2

755

Sample Input 3

549
817
715
603

Sample Output 3

1152

Problem Statement

Some number of chocolate pieces were prepared for a training camp. The camp had N participants and lasted for D days. The i-th participant (1 \leq i \leq N) ate one chocolate piece on each of the following days in the camp: the 1-st day, the (A_i + 1)-th day, the (2A_i + 1)-th day, and so on. As a result, there were X chocolate pieces remaining at the end of the camp. During the camp, nobody except the participants ate chocolate pieces.

Find the number of chocolate pieces prepared at the beginning of the camp.

Constraints

• 1 \leq N \leq 100
• 1 \leq D \leq 100
• 1 \leq X \leq 100
• 1 \leq A_i \leq 100 (1 \leq i \leq N)
• All input values are integers.

Sample Input 1

3
7 1
2
5
10

Sample Output 1

8

The camp has 3 participants and lasts for 7 days. Each participant eats chocolate pieces as follows:

• The first participant eats one chocolate piece on Day 1, 3, 5 and 7, for a total of four.
• The second participant eats one chocolate piece on Day 1 and 6, for a total of two.
• The third participant eats one chocolate piece only on Day 1, for a total of one.

Since the number of pieces remaining at the end of the camp is one, the number of pieces prepared at the beginning of the camp is 1 + 4 + 2 + 1 = 8.

Sample Input 2

2
8 20
1
10

Sample Output 2

29

Sample Input 3

5
30 44
26
18
81
18
6

Sample Output 3

56

Problem Statement

There are N sightseeing spots on the x-axis, numbered 1, 2, ..., N. Spot i is at the point with coordinate A_i. It costs |a - b| yen (the currency of Japan) to travel from a point with coordinate a to another point with coordinate b along the axis.

You planned a trip along the axis. In this plan, you first depart from the point with coordinate 0, then visit the N spots in the order they are numbered, and finally return to the point with coordinate 0.

However, something came up just before the trip, and you no longer have enough time to visit all the N spots, so you decided to choose some i and cancel the visit to Spot i. You will visit the remaining spots as planned in the order they are numbered. You will also depart from and return to the point with coordinate 0 at the beginning and the end, as planned.

For each i = 1, 2, ..., N, find the total cost of travel during the trip when the visit to Spot i is canceled.

Constraints

• 2 \leq N \leq 10^5
• -5000 \leq A_i \leq 5000 (1 \leq i \leq N)
• All input values are integers.

Sample Input 1

3
3 5 -1

Sample Output 1

12
8
10

Spot 1, 2 and 3 are at the points with coordinates 3, 5 and -1, respectively. For each i, the course of the trip and the total cost of travel when the visit to Spot i is canceled, are as follows:

• For i = 1, the course of the trip is 0 \rightarrow 5 \rightarrow -1 \rightarrow 0 and the total cost of travel is 5 + 6 + 1 = 12 yen.
• For i = 2, the course of the trip is 0 \rightarrow 3 \rightarrow -1 \rightarrow 0 and the total cost of travel is 3 + 4 + 1 = 8 yen.
• For i = 3, the course of the trip is 0 \rightarrow 3 \rightarrow 5 \rightarrow 0 and the total cost of travel is 3 + 2 + 5 = 10 yen.

Sample Input 2

5
1 1 1 2 0

Sample Output 2

4
4
4
2
4

Sample Input 3

6
-679 -2409 -3258 3095 -3291 -4462

Sample Output 3

21630
21630
19932
8924
21630
19288

Problem Statement

You are given two integers A and B.

Print a grid where each square is painted white or black that satisfies the following conditions, in the format specified in Output section:

• Let the size of the grid be h \times w (h vertical, w horizontal). Both h and w are at most 100.
• The set of the squares painted white is divided into exactly A connected components.
• The set of the squares painted black is divided into exactly B connected components.

It can be proved that there always exist one or more solutions under the conditions specified in Constraints section. If there are multiple solutions, any of them may be printed.

Notes

Two squares painted white, c_1 and c_2, are called connected when the square c_2 can be reached from the square c_1 passing only white squares by repeatedly moving up, down, left or right to an adjacent square.

A set of squares painted white, S, forms a connected component when the following conditions are met:

• Any two squares in S are connected.
• No pair of a square painted white that is not included in S and a square included in S is connected.

A connected component of squares painted black is defined similarly.

Constraints

• 1 \leq A \leq 500
• 1 \leq B \leq 500

Sample Input 1

2 3

Sample Output 1

3 3
##.
..#
#.#

This output corresponds to the grid below:

Sample Input 2

7 8

Sample Output 2

3 5
#.#.#
.#.#.
#.#.#

Sample Input 3

1 1

Sample Output 3

4 2
..
#.
##
##

Sample Input 4

3 14

Sample Output 4

8 18
..................
..................
....##.......####.
....#.#.....#.....
...#...#....#.....
..#.###.#...#.....
.#.......#..#.....
#.........#..####.