21609_HospitalAgain

Theme hospital? Yes, it’s theme hospital again!

The hospital has n doctors and divides into four groups. Every group would be changed during the patients’ medical care. Each doctor has his own number and the doctors can belong to all the groups.

At the first day when the hospital open, the doctors would divide into four groups according to their own number. So if the total number of four groups are gug2,g3,g4, and then the doctors will divide as this:

Group 1: 1, 2, ..., g₁

Group 2: g₁+1, g₁+2, ..., g₁+g₂

Group 3: g₁+g₂+1, g₁+g₂+2, ..., g₁+g₂+g₃

Group 4: g₁+g₂+g₃+1, g₁+g₂+g₃+2, ..., g₁+g₂+g₃+g₄

And then, the first patient will choose doctor 1, and when the doctor 1 finished, he will go to the last position of group 2. The second patient will choose doctor g₁+1, and when finished, the doctor will go the last position of group 3... The k-th patient will choose the first doctor of group k%4, and when finished, the doctor will go the last position of group (k+1)%4.

The hospital will have m patients in one day. And before another day begins, the doctors will also divide into the four groups according to the last day. They will just combine the four groups, and then divide into four groups into g₁, g₂, g₃ and g₄. So if the end of the day is:

Group 1: d₁, d₂, ..., d_k1                  Group 2: d_k1+1, d_k1+2, ..., d_k2

Group 3: d_k2+1, d_k2+2 , ..., d_k3         Group 4: d_k3+1, d_k3+2, ..., d_k4

Then they combine into

d₁, d₂, ..., d_k1, d_k1+1, d_k1+2, ..., d_k2, d_k2+1, d_k2+2, ..., d_k3, d_k3+1, d_k3+2, ..., d_k4

And at last, they divide into four groups again:

Group 1: d₁, d₂, ..., d_g1

Group 2: d_g1+1, d_g1+2, ..., d_g1+g2

Group 3: d_g1+g2+1, d_g1+g2+2, ..., d_g1+g2+g3

Group 4: d_g1+g2+g3+1, d_g1+g2+g3+2, ..., d_g1+g2+g3+g4

After that, the patients will choose the doctors just the same as the first day and so on.

After a few days,at the beginning of the day, the doctors' arrange will just same as the first day!

Can you tell me when it comes?

This problem contains multiply test cases. In each test cases, there are five integers g₁, g₂, g₃, g₄, p ( 1 ≤ g₁, g₂, g₃, g₄ ≤ 20, p ≤ 10000 ) per line, that stands for the number of group 1, group 2, group 3, group 4 and the total patients in one day.

The input will terminated by g₁=g₂=g₃=g₄=p=0 and the number of test cases will not exceed 12000.

Print one line of an integer what is the meaning of at this day, the doctors will same as the first day. The answer will not exceed 2³¹.

2 1 1 1 6
0 0 0 0 0

3

At first day, no patients come would be    g₁: 1  2     g₂:3     g₃:4     g₄:5

1 patients: g₁:2       g₂:3  1    g₃:4       g₄:5

2 patients: g₁:2       g₂:1        g₃:4  3   g₄:5

3 patients: g₁:2       g₂:1        g₃:3       g₄:5  4

4 patients: g₁:2  5   g₂:1        g₃:3       g₄:4

5 patients: g₁:5       g₂:1  2    g₃:3       g₄:4

6 patients: g₁:5       g₂:2        g₃:3  1   g₄:4

So after one day: the four groups will be   g1:5  2     g2:3     g3:1     g₄:4

After 2 day: g₁:4  2     g₂:3     g₃:5     g₄:1

After 3 day: g₁:1  2     g₂:3     g₃:4     g₄:5