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.