Besides George Plover's house stands a farm. The farm can be described as an  matrix. The growth rate of weed in row 
 and column 
 is denoted as 
.  In this problem, two arrays 
 and 
 will be given. And for all 
, 
 , 
.
 The growth rate  indicates that the weed will grow 
 units every second. At the moment 
, there is no weed on the farm.
 George will use mower  times, where the 
-th use occurs at the moment 
. Each use of the mower completely removes weeds in a row or a column.
 George wonders how many units of weed he will remove.
 The answer might be very large, so please output the desired answer modulo . 
The first line contains two integers
and
.
The second line containsintegers, where the
-th integer is
.
The third line containsintegers, where the
-th integer is
.
The next line contains an integer.
Each of the nextlines contains three integers.
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: George clears the weeds in row
at the moment
.
![]()
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: George clears the weeds in column
at the moment
.
,
.
It is guaranteed that,
,
and
is strictly increasing with lines.
Output one integer indicating the answer modulo.