Problem Statement

In one section of Santa Claus's warehouse, cube-shaped gift boxes are stacked.
This section is a grid of $H$ cells in the north-south direction and $W$ cells in the east-west direction, and each cell has the same size as a gift box.
Each cell of the grid has $0$ or more gift boxes stacked on it.
Viewing this grid from the west reveals that, for the cells lined up in the east-west direction in the $i$-th row from the north $(1\le i\le H)$, the maximum number of gift boxes stacked is $A_i$.
Similarly, viewing this grid from the south reveals that, for the cells lined up in the north-south direction in the $j$-th column from the west $(1\le j\le W)$, the maximum number of gift boxes stacked is $B_j$.
Find the minimum and maximum among the possible total numbers of gift boxes stacked in the grid.
Since the answers can be very large, output them modulo $10^9+7$.

Constraints

• $1\le H\le 10^5$
• $1\le W\le 10^5$
• $0\le A_i,B_j\le 10^9$
• There exists a way of stacking gift boxes that satisfies the conditions
• All inputs are integers

Input

The input is given from standard input in the following format.

$H\ W$
$A_1\ A_2\ \dots\ A_H$
$B_1\ B_2\ \dots\ B_W$

Output

Output $2$ lines.
On line $1$, output the minimum.
On line $2$, output the maximum.

Sample

3 5
1 3 2
0 1 3 2 1

7
17

4 3
100000000 100000000 100000000 100000000
100000000 100000000 100000000

400000000
199999993

5 4
1 1 1 1 4
1 2 2 4

12
25

12 16
54 70 63 91 44 64 56 75 62 69 49 74
82 43 72 3 63 82 56 91 56 4 47 1 54 64 79 48

1288
8899