Problem:
Score : 1000 points

Problem Statement

Snuke participated in a magic show.

A magician prepared N identical-looking boxes.
He put a treasure in one of the boxes, closed the boxes, shuffled them, and numbered them 1 through N.

Since the boxes are shuffled, now Snuke has no idea which box contains the treasure.
Snuke wins the game if he opens a box containing the treasure.
You may think that if Snuke opens all boxes at once, he can always win the game.
However, there are some tricks:

Snuke must open the boxes one by one. After he opens a box and checks the content of the box, he must close the box before opening the next box.

He is only allowed to open Box i at most a_i times.

The magician may secretly move the treasure from a closed box to another closed box, using some magic trick.
For simplicity, assume that the magician never moves the treasure while Snuke is opening some box.
However, he can move it at any other time (before Snuke opens the first box, or between he closes some box and opens the next box).

The magician can perform the magic trick at most K times.

Can Snuke always win the game, regardless of the initial position of the treasure and the movements of the magician?

Constraints

2 \leq N \leq 50

1 \leq K \leq 50

1 \leq a_i \leq 100

Input

Input is given from Standard Input in the following format:

N K
a_1 a_2 \cdots a_N

Output

If the answer is no, print a single -1.

Otherwise, print one possible move of Snuke in the following format:

Q
x_1 x_2 \cdots x_Q

It means that he opens boxes x_1, x_2, \cdots, x_Q in this order.

In case there are multiple possible solutions, you can output any.

Sample Input 1

2 1
5 5

Sample Output 1

7
1 1 2 1 2 2 1

If Snuke opens the boxes 7 times in the order 1 \rightarrow 1 \rightarrow 2 \rightarrow 1 \rightarrow 2 \rightarrow 2 \rightarrow 1, he can always find the treasure regardless of its initial position and the movements of the magician.

Sample Input 2

3 50
5 10 15

Sample Output 2

-1

Solution in Fortran (gfortran v4.8.4) (judge verdict: Wrong Answer)

program test
integer(8) :: nn,k,aa(100),aaa(100),a(100),b(100),c(10000),i,a_min,atai,sig,last(100),j,count,temp


read(*,*) nn,k
read(*,*) (aa(i),i=1,nn)

a(1:nn) = aa(1:nn)

do i = 1,nn
	b(i) = i
enddo

call heapsort2(nn,a(1:nn),b(1:nn))


count = 1

do i = 1,k
	aaa(1:nn) = aa(1:nn)

	if(last(i-1) > 0 )then
		aaa(last(i-1)) = 999
	endif
	
	minimum = 999999
	do j =1,nn
		if(aaa(j) <= minimum) then
			last(i) = j
			minimum = aaa(j)
		endif
	enddo

	do j=1,nn
		if(i==1) then
			if((j .ne. last(i))) then
				c(count) = j
				count = count + 1
			endif
		else
			if((j .ne. last(i-1)) .and. (j .ne. last(i))) then
				c(count) = j
				count = count + 1
			endif
		endif
	enddo

	do j=1,nn
		if(j == last(i)) then
			c(count) = j
			count = count + 1
		endif
	enddo

enddo

	do j=1,nn
		if(j .ne. last(k)) then
			c(count) = j
			count = count + 1
		endif
	enddo

if( sum(a(1:nn))<nn*(k+1)-k .or. a(1)<1+k/2 ) then
	write(*,*) -1
else
	write(*,*) count-1
	write(*,*) c(1:count-1)
endif









contains
 
subroutine heapsort2(n,y1,y2)
 
	implicit none
	integer(8),intent(in) :: n
	integer(8),intent(inout) :: y1(1:n)
	integer(8),intent(inout) :: y2(1:n)
	integer(8) :: i,k,j,l
	integer(8) :: t1,t2
	
	l = n/2+1
	k = n
 
	do while (k /= 1)
		 if(l > 1) then
				l = l-1
				t1 = y1(l)
				t2 = y2(l)
				
		 else
				t1 = y1(k)
				t2 = y2(k)
				y1(k) = y1(1)
				y2(k) = y2(1)
				k = k-1
				if(k == 1) then
					 y1(1) = t1
					 y2(1) = t2
					 exit
				endif
		 endif
 
		 i = l
		 j = l+l
 
		 do while(j <= k)
				if(j < k) then
					 if(y1(j) < y1(j+1)) j = j+1
				endif
				
				if (t1 < y1(j)) then
					 y1(i) = y1(j)
					 y2(i) = y2(j)
					 i = j
					 j = j+j
				else
					 j = k+1
				endif
		 
		 enddo
		 
		 y1(i) = t1
		 y2(i) = t2
	
	enddo
	return
 
end subroutine heapsort2

end program