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.

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.

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.

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.