B. Better Die
time limit per test
1 second
memory limit per test
512 megabytes
input
standard input
output
standard output

You have a fair six-sided die with positive integer face values $$$a_1,a_2,\ldots,a_6$$$. Construct another fair six-sided die with positive integer face values $$$b_1,b_2,\ldots,b_6$$$ whose sum is exactly $$$k$$$. Face values may repeat on either die.

Roll each die once, independently. The new die wins if and only if its value is strictly greater than the original die's value; a tie is not a win. Determine whether you can make it win at least $$$19$$$ of the $$$36$$$ equally likely pairs of faces (that is, with probability strictly greater than $$$50\%$$$). If so, construct such a die.

Input

The first line contains six integers $$$a_1,a_2,\ldots,a_6$$$ ($$$1\le a_i\le 10^9$$$), the labels of the original die.

The second line contains an integer $$$k$$$ ($$$1\le k\le 10^{18}$$$), the required sum of the new die's labels.

Output

If no valid new die exists, print NO.

Otherwise, print YES on the first line and six positive integers $$$b_1,b_2,\ldots,b_6$$$ on the second line. Their sum must be exactly $$$k$$$, and the new die must win at least $$$19$$$ of the $$$36$$$ pairs of faces.

The labels may appear in any order. If multiple answers exist, print any one. The strings YES and NO are case-sensitive.

Examples
Input
1 2 3 4 5 6
25
Output
YES
1 1 2 7 7 7
Input
1 1 1 1 1 1
9
Output
NO
Note

For the first example, another valid choice of labels is $$$5,4,4,4,4,4$$$. These labels sum to $$$5+4+4+4+4+4=25$$$. Its face labeled $$$5$$$ beats four faces of the original die, and each face labeled $$$4$$$ beats three. Thus, it wins $$$4+5\cdot3=19$$$ pairs.

In the second example, a face must be labeled at least $$$2$$$ to win. Each such face wins six pairs, so at least four are needed to win $$$19$$$ pairs. Even if the other two faces are labeled $$$1$$$, the sum is at least $$$2+2+2+2+1+1=10 \gt 9$$$.