Polycarp is a regular customer at the restaurant "Ber Patio". He likes having lunches there.

"Ber Patio" has special discount program for regular customers. A customer can collect bonuses and partially cover expenses in the restaurant.

Let's assume a customer currently has b bonuses and she has to pay r burles for a lunch. In this case the customer can use bonuses (1 bonus = 1 burle) to reduce the payment. She can cover at most half of the payment using bonuses. However, 1 bonus will be added to the customer's bonus balance per each 10 burles she paid.

Formally:

a customer can choose any number x of bonuses to use ( $\text{[math]}$ )),
the customer's bonus balance is reduced by x,
the customer pays r - x burles,
the customer's bonus balance is increased by ⌊(r - x) / 10⌋ (i.e. integer division rounded down is used).

Initially, there are b bonuses on Polycarp's account. Polycarp is going to have a lunch in "Ber Patio" for the next n days. He estimated the values a₁, a₂, ..., a_n, where a_i is the number of burles in a receipt for the i-th day. The sum over all receipts doesn't exceed 10⁵ burles.

Write a program to find the minimum number of burles Polycarp has to spend and an optimal strategy to use bonuses.

Input

The first line contains two integer numbers n and b (1 ≤ n ≤ 5000, 0 ≤ b ≤ 10⁵) — number of days and initial number of bonuses Polycarp has.

The second line contains the integer sequence a₁, a₂, ..., a_n (1 ≤ a_i ≤ 1000), where a_i is the amount of burles in the i-th day's receipt.

It is guaranteed that the sum of all receipts does not exceed 10⁵ burles.

Output

On the first line, print the expected minimal number of burles to pay for all n receipts.

On the second line, print the sequence of integer numbers b₁, b₂, ..., b_n, where b_i is the number of bonuses to use on the i-th day. If there are multiple solutions, print any of them.

Ber Patio

Examples