1945: Ber Patio
Description
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 (
)), - 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,...,an, where ai 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.
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,...,an (1≤ai≤1000), where ai 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.
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,...,bn, where bi is the number of bonuses to use on the i-th day. If there are multiple solutions, print any of them.
3 21
12 75 52
110
2 5 22
3 39
58 64 33
107
28 4 16