Problem Statement

Takahashi runs AtCoder store.
N customers visit the store, and M items are sold in the store.
The motivation of the $i-th (1\leq i\leq N)$ customer is B _ i.
The value of the $j-th (1\leq j\leq M)$ item is C _ j.
Takahashi sets a price for each item.
The i-th customer buys one j-th item if and only if its price P _ j satisfies:

• $B _ i+C _ j\geq P _ j$.

For each $j=1,2,\ldots,M,$ find the gross sale of the j-th item when Takahashi sets the price so that the sale is maximized.
The gross sale of the j-th item is defined as the product of P _ j and the number of customers that buys the j-th item.

Input

The input is given from Standard Input in the following format:
N M
$B _ 1 B _ 2 \ldots B _ N$
$C _ 1 C _ 2 \ldots C _ M$

Output

Print a line containing the gross sale of the j-th item for each $j=1,2,\ldots,M,$ separated by spaces.

Constraints

• $1\leq N\leq2\times10^5$
• $1\leq M\leq2\times10^5$
• $0\leq B _ i\leq10^9\quad(1\leq i\leq N)$
• $0\leq C _ i\leq10^9\quad(1\leq i\leq M)$
• All values in the input are integers.

Sample Input 1

5 4
100 200 300 400 500
120 370 470 80

Sample Output 1

1280 2350 2850 1140

For example, he may set the price of the 1-st item to 320; then the 2-nd, 3-rd, 4-th, and 5-th customers will buy one.
The gross sale of the 1-st item will be 1280.
Since he cannot make the gross sale of the 1-st item greater than 1280, the 1-st value to be printed is 1280.

Sample Input 2

4 4
0 2 10 2
13 13 0 4

Sample Output 2

52 52 10 18

Two customers may have the same motivation. Also, two items may have the same value.

Sample Input 3

12 15
16 592 222 983 729 338 747 61 451 815 838 281
406 319 305 519 317 590 507 946 365 5 673 478 340 176 2

Sample Output 3

6280 5466 5382 7410 5454 8120 7290 11680 5870 3670 8950 7000 5620 4608 3655

Sample Input 4

5 5
1000000000 1000000000 1000000000 1000000000 1000000000
1000000000 1000000000 1000000000 1000000000 1000000000

Sample Output 4

10000000000 10000000000 10000000000 10000000000 10000000000

Note that the gross sales may not fit into a 32-bit integer type.

见题面 Input 部分

见题面 Output 部分