Dreamoon and Sets (Codeforces 476D)
Tags: Math, constructive algorithms

Dreamoon likes to play with sets, integers and .  is defined as the largest positive integer that divides both a and b.Let S be a set of exactly four distinct integers greater than 0. Define S to be of rank k if and only if for all pairs of distinct elements si, sj from S, .Given k and n, Dreamoon wants to make up n sets of rank k using integers from 1 to m such that no integer is used in two different sets (of course you can leave some integers without use). Calculate the minimum m that makes it possible and print one possible solution.

Input: The single line of the input contains two space separated integers n, k (1 ≤ n ≤ 10 000, 1 ≤ k ≤ 100).

Output: On the first line print a single integer — the minimal possible m. On each of the next n lines print four space separated integers representing the i-th set.Neither the order of the sets nor the order of integers within a set is important. If there are multiple possible solutions with minimal m, print any one of them.

Note: For the first example it's easy to see that set {1, 2, 3, 4} isn't a valid set of rank 1 since .

Sample Inputs:
1 1

2 2

Sample Outputs:
5
1 2 3 5

22
2 4 6 22
14 18 10 16

Solution (Python):
(n, k) = map(int, input('').split(' '))
print(str((3 * n + 3 * n) * k - k))
for i in range(1, n + 1):
    ans = ''
    ans += str(6 * i * k - 5 * k)
    ans += ' '
    ans += str(6 * i * k - 4 * k)
    ans += ' '
    ans += str(6 * i * k - 3 * k)
    ans += ' '
    ans += str(6 * i * k - k)
    print(ans)

Solution (Python):
(n, k) = map(int, input('').split(' '))
print(str((3 * n + 3 * n) * k - k))
for i in range(1, n + 1):
    ans = ''
    ans += str(6 * i * k - 5 * k)
    ans += ' '
    ans += str(6 * i * k - 4 * k)
    ans += ' '
    ans += str(6 * i * k - 3 * k)
    ans += ' '
    ans += str(6 * i * k - k)
    print(ans)

Solution (Python):
(n, k) = map(int, input().split())
print((6 * n - 1) * k)
print('\n'.join(('%i %i %i %i' % tuple((k * (6 * i + j) for j in (1, 2, 3, 5))) for i in range(n))))