Cake 123

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.

Input

Input is given from Standard Input in the following format:

X Y Z K A_1 \ A_2 \ A_3 \ ... \ A_X B_1 \ B_2 \ B_3 \ ... \ B_Y C_1 \ C_2 \ C_3 \ ... \ C_Z

Output

Print K lines. The i-th line should contain the i-th value stated in the problem statement.

Examples

Input

2 2 2 8 4 6 1 5 3 8

Output

19 17 15 14 13 12 10 8

Input

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

Output

400 310 310 301 301

Input

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

Output

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

inputFormat

input are integers.

Input

Input is given from Standard Input in the following format:

X Y Z K A_1 \ A_2 \ A_3 \ ... \ A_X B_1 \ B_2 \ B_3 \ ... \ B_Y C_1 \ C_2 \ C_3 \ ... \ C_Z

outputFormat

Output

Print K lines. The i-th line should contain the i-th value stated in the problem statement.

Examples

Input

2 2 2 8 4 6 1 5 3 8

Output

19 17 15 14 13 12 10 8

Input

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

Output

400 310 310 301 301

Input

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

Output

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

样例

2 2 2 8
4 6
1 5
3 8

19
17
15
14
13
12
10
8

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