Problem Statement

In AtCoder city, there are five antennas standing in a straight line. They are called Antenna A, B, C, D and E from west to east, and their coordinates are a, b, c, d and e, respectively.
Two antennas can communicate directly if the distance between them is k or less, and they cannot if the distance is greater than k.
Determine if there exists a pair of antennas that cannot communicate directly.
Here, assume that the distance between two antennas at coordinates p and q (p < q) is q - p.

Constraints

• a, b, c, d, e and k are integers between 0 and 123 (inclusive).
• a < b < c < d < e

Sample Input 1

1
2
4
8
9
15

Sample Output 1

Yay!

In this case, there is no pair of antennas that cannot communicate directly, because:

• the distance between A and B is 2 - 1 = 1
• the distance between A and C is 4 - 1 = 3
• the distance between A and D is 8 - 1 = 7
• the distance between A and E is 9 - 1 = 8
• the distance between B and C is 4 - 2 = 2
• the distance between B and D is 8 - 2 = 6
• the distance between B and E is 9 - 2 = 7
• the distance between C and D is 8 - 4 = 4
• the distance between C and E is 9 - 4 = 5
• the distance between D and E is 9 - 8 = 1

and none of them is greater than 15. Thus, the correct output is Yay!.

Sample Input 2

15
18
26
35
36
18

Sample Output 2

:(

In this case, the distance between antennas A and D is 35 - 15 = 20 and exceeds 18, so they cannot communicate directly. Thus, the correct output is :(.

Problem Statement

The restaurant AtCoder serves the following five dishes:

• ABC Don (rice bowl): takes A minutes to serve.
• ARC Curry: takes B minutes to serve.
• AGC Pasta: takes C minutes to serve.
• APC Ramen: takes D minutes to serve.
• ATC Hanbagu (hamburger patty): takes E minutes to serve.

Here, the time to serve a dish is the time between when an order is placed and when the dish is delivered.

This restaurant has the following rules on orders:

• An order can only be placed at a time that is a multiple of 10 (time 0, 10, 20, ...).
• Only one dish can be ordered at a time.
• No new order can be placed when an order is already placed and the dish is still not delivered, but a new order can be placed at the exact time when the dish is delivered.

E869120 arrives at this restaurant at time 0. He will order all five dishes. Find the earliest possible time for the last dish to be delivered.
Here, he can order the dishes in any order he likes, and he can place an order already at time 0.

Constraints

• A, B, C, D and E are integers between 1 and 123 (inclusive).

Sample Input 1

29
20
7
35
120

Sample Output 1

215

If we decide to order the dishes in the order ABC Don, ARC Curry, AGC Pasta, ATC Hanbagu, APC Ramen, the earliest possible time for each order is as follows:

• Order ABC Don at time 0, which will be delivered at time 29.
• Order ARC Curry at time 30, which will be delivered at time 50.
• Order AGC Pasta at time 50, which will be delivered at time 57.
• Order ATC Hanbagu at time 60, which will be delivered at time 180.
• Order APC Ramen at time 180, which will be delivered at time 215.

There is no way to order the dishes in which the last dish will be delivered earlier than this.

Sample Input 2

101
86
119
108
57

Sample Output 2

481

If we decide to order the dishes in the order AGC Pasta, ARC Curry, ATC Hanbagu, APC Ramen, ABC Don, the earliest possible time for each order is as follows:

• Order AGC Pasta at time 0, which will be delivered at time 119.
• Order ARC Curry at time 120, which will be delivered at time 206.
• Order ATC Hanbagu at time 210, which will be delivered at time 267.
• Order APC Ramen at time 270, which will be delivered at time 378.
• Order ABC Don at time 380, which will be delivered at time 481.

There is no way to order the dishes in which the last dish will be delivered earlier than this.

Sample Input 3

123
123
123
123
123

Sample Output 3

643

This is the largest valid case.

Problem Statement

In 2028 and after a continuous growth, AtCoder Inc. finally built an empire with six cities (City 1, 2, 3, 4, 5, 6)!

There are five means of transport in this empire:

• Train: travels from City 1 to 2 in one minute. A train can occupy at most A people.
• Bus: travels from City 2 to 3 in one minute. A bus can occupy at most B people.
• Taxi: travels from City 3 to 4 in one minute. A taxi can occupy at most C people.
• Airplane: travels from City 4 to 5 in one minute. An airplane can occupy at most D people.
• Ship: travels from City 5 to 6 in one minute. A ship can occupy at most E people.

For each of them, one vehicle leaves the city at each integer time (time 0, 1, 2, ...).

There is a group of N people at City 1, and they all want to go to City 6.
At least how long does it take for all of them to reach there? You can ignore the time needed to transfer.

Constraints

• 1 \leq N, A, B, C, D, E \leq 10^{15}
• All values in input are integers.

Sample Input 1

5
3
2
4
3
5

Sample Output 1

7

One possible way to travel is as follows. First, there are N = 5 people at City 1, as shown in the following image:

In the first minute, three people travels from City 1 to City 2 by train. Note that a train can only occupy at most three people.

In the second minute, the remaining two people travels from City 1 to City 2 by train, and two of the three people who were already at City 2 travels to City 3 by bus. Note that a bus can only occupy at most two people.

In the third minute, two people travels from City 2 to City 3 by train, and another two people travels from City 3 to City 4 by taxi.

From then on, if they continue traveling without stopping until they reach City 6, all of them can reach there in seven minutes.
There is no way for them to reach City 6 in 6 minutes or less.

Sample Input 2

10
123
123
123
123
123

Sample Output 2

5

All kinds of vehicles can occupy N = 10 people at a time. Thus, if they continue traveling without stopping until they reach City 6, all of them can reach there in five minutes.

Sample Input 3

10000000007
2
3
5
7
11

Sample Output 3

5000000008

Note that the input or output may not fit into a 32-bit integer type.

Problem Statement

The Patisserie AtCoder sells cakes with number-shaped candles. There are X, Y and Z kinds of cakes with 1-shaped, 2-shaped and 3-shaped candles, respectively. Each cake has an integer value called deliciousness, as follows:

• The deliciousness of the cakes with 1-shaped candles are A_1, A_2, ..., A_X.
• The deliciousness of the cakes with 2-shaped candles are B_1, B_2, ..., B_Y.
• The deliciousness of the cakes with 3-shaped candles are C_1, C_2, ..., C_Z.

Takahashi decides to buy three cakes, one for each of the three shapes of the candles, to celebrate ABC 123.
There are X \times Y \times Z such ways to choose three cakes.
We will arrange these X \times Y \times Z ways in descending order of the sum of the deliciousness of the cakes.
Print the sums of the deliciousness of the cakes for the first, second, ..., K-th ways in this list.

Constraints

• 1 \leq X \leq 1 \ 000
• 1 \leq Y \leq 1 \ 000
• 1 \leq Z \leq 1 \ 000
• 1 \leq K \leq \min(3 \ 000, X \times Y \times Z)
• 1 \leq A_i \leq 10 \ 000 \ 000 \ 000
• 1 \leq B_i \leq 10 \ 000 \ 000 \ 000
• 1 \leq C_i \leq 10 \ 000 \ 000 \ 000
• All values in input are integers.

Sample Input 1

2 2 2 8
4 6
1 5
3 8

Sample Output 1

19
17
15
14
13
12
10
8

There are 2 \times 2 \times 2 = 8 ways to choose three cakes, as shown below in descending order of the sum of the deliciousness of the cakes:

• (A_2, B_2, C_2): 6 + 5 + 8 = 19
• (A_1, B_2, C_2): 4 + 5 + 8 = 17
• (A_2, B_1, C_2): 6 + 1 + 8 = 15
• (A_2, B_2, C_1): 6 + 5 + 3 = 14
• (A_1, B_1, C_2): 4 + 1 + 8 = 13
• (A_1, B_2, C_1): 4 + 5 + 3 = 12
• (A_2, B_1, C_1): 6 + 1 + 3 = 10
• (A_1, B_1, C_1): 4 + 1 + 3 = 8

Sample Input 2

3 3 3 5
1 10 100
2 20 200
1 10 100

Sample Output 2

400
310
310
301
301

There may be multiple combinations of cakes with the same sum of the deliciousness. For example, in this test case, the sum of A_1, B_3, C_3 and the sum of A_3, B_3, C_1 are both 301. However, they are different ways of choosing cakes, so 301 occurs twice in the output.

Sample Input 3

10 10 10 20
7467038376 5724769290 292794712 2843504496 3381970101 8402252870 249131806 6310293640 6690322794 6082257488
1873977926 2576529623 1144842195 1379118507 6003234687 4925540914 3902539811 3326692703 484657758 2877436338
4975681328 8974383988 2882263257 7690203955 514305523 6679823484 4263279310 585966808 3752282379 620585736

Sample Output 3

23379871545
22444657051
22302177772
22095691512
21667941469
21366963278
21287912315
21279176669
21160477018
21085311041
21059876163
21017997739
20703329561
20702387965
20590247696
20383761436
20343962175
20254073196
20210218542
20150096547

Note that the input or output may not fit into a 32-bit integer type.