$mod=1e9+7;

$m=<>+1;
$/=$";
$v=$_,$m-=$_+1,++$h for <>;
exit!print 1 if $v==0;
exit!print "NA" if $m<0;

$x=1;
for(1..$m){
	$x=$x*($h+$_)%$mod*($i[$_]=$i[$mod%$_]*($mod-int($mod/$_))%$mod||1)%$mod;
}
print $x;