To help plan his fishing trip, John has gathered some information about the lakes. For each lake i, the number of fish expected to be caught in the initial 5 minutes, denoted fi (fi >= 0), is known. Each 5 minutes of fishing decreases the number of fish expected to be caught in the next 5-minute interval by a constant rate of di (di >= 0). If the number of fish expected to be caught in an interval is less than or equal to di, there will be no more fish left in the lake in the next interval. To simplify the planning, John assumes that no one else will be fishing at the lakes to affect the number of fish he expects to catch.

Write a program to help John plan his fishing trip to maximize the number of fish expected to be caught. The number of minutes spent at each lake must be a multiple of 5.

**This problem contains multiple test cases!**

The first line of a multiple input is an integer N, then a blank line followed by N input blocks. Each input block is in the format indicated in the problem description. There is a blank line between input blocks.

The output format consists of N output blocks. There is a blank line between output blocks.

**Input**

You will be given a number of cases in the input. Each case starts with a line
containing n. This is followed by a line containing h. Next, there is a line
of n integers specifying fi (1 <= i <= n), then a line of n integers di
(1 <= i <= n), and finally, a line of n - 1 integers ti (1 <= i <=
n-1). Input is terminated by a case in which n = 0.

**Output **

For each test case, print the number of minutes spent at each lake, separated
by commas, for the plan achieving the maximum number of fish expected to be
caught (you should print the entire plan on one line even if it exceeds 80 characters).
This is followed by a line containing the number of fish expected. If multiple
plans exist, choose the one that spends as long as possible at lake 1, even
if no fish are expected to be caught in some intervals. If there is still a
tie, choose the one that spends as long as possible at lake 2, and so on. Insert
a blank line between cases.

**Sample Input **

1

2

1

10 1

2 5

2

4

4

10 15 20 17

0 3 4 3

1 2 3

4

4

10 15 50 30

0 3 4 3

1 2 3

0

**Sample Output**

45, 5

Number of fish expected: 31

240, 0, 0, 0

Number of fish expected: 480

115, 10, 50, 35

Number of fish expected: 724