### 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.

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.

52 52 10 18

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