Note

The problems of yukicoder contest 279 (Zelkova and Cherry) are not sorted in order of difficulty. Therefore, we strongly recommend choosing which problems to attempt based on publicly available information such as the problem statements, the number of stars indicating difficulty, and the number of solvers.

Problem Statement

There are four sequences $\mathbb{A}=(A_w)_{w=1}^K, \mathbb{B}=(B_x)_{x=1}^L ,\mathbb{C}=(C_y)_{y=1}^M, \mathbb{D}=(D_z)_{z=1}^N$ of lengths $K,L,M,N$, respectively. From these four sequences, define the quadruple-indexed sequence $\mathbb{E}=(E_{w,x,y,z})_{w,x,y,z}$ by $E_{w,x,y,z}=A_w B_x C_y D_z$.

The sequence $\mathbb{E}$ has $KLMN$ elements in total. When these elements are sorted in ascending order, find the number $T$ that is the $S$-th from the smallest, and give one each of the elements $a,b,c,d$ of the sequences $\mathbb{A},\mathbb{B},\mathbb{C},\mathbb{D}$ that satisfy $T=abcd$.

Constraints

• $1 \leq K,L,M,N \leq 600$
• $1 \leq S \leq KLMN$
• $-3 \times 10^4 \leq A_w,B_x,C_y,D_z \leq 3 \times 10^4$
• All input values are integers.

Input

$K\ L\ M\ N\ S$
$A_1\ \dots A_K$
$B_1\ \dots B_L$
$C_1\ \dots C_M$
$D_1\ \dots D_N$

Output

When the $S$-th number of the quadruple sequence $\mathbb{E}$ sorted in ascending order is $T$, and the elements $a,b,c,d$ of $\mathbb{A},\mathbb{B},\mathbb{C},\mathbb{D}$ satisfy $T=abcd$, output them as follows.

$T$
$a\ b\ c\ d$

Sample

1 1 2 3 4
-1
2
-3 4
-5 6 -7

36
-1 2 -3 6

1 2 3 4 12
1
1 1
1 1 1
1 1 1 1

1
1 1 1 1

8 8 8 8 2000
3 1 4 1 5 9 2 6
5 3 5 8 9 7 9 3
2 3 8 4 6 2 6 4
3 3 8 3 2 7 9 5

288
2 3 6 8