Problem:
Score : 300 points

Problem Statement

You've come to your favorite store Infinitesco to buy some ice tea.

The store sells ice tea in bottles of different volumes at different costs.
Specifically, a 0.25-liter bottle costs Q yen, a 0.5-liter bottle costs H yen, a 1-liter bottle costs S yen, and a 2-liter bottle costs D yen.
The store has an infinite supply of bottles of each type.

You want to buy exactly N liters of ice tea. How many yen do you have to spend?

Constraints

1 \leq Q, H, S, D \leq 10^8

1 \leq N \leq 10^9

All input values are integers.

Input

Input is given from Standard Input in the following format:

Q H S D
N

Output

Print the smallest number of yen you have to spend to buy exactly N liters of ice tea.

Sample Input 1

20 30 70 90
3

Sample Output 1

150

Buy one 2-liter bottle and two 0.5-liter bottles. You'll get 3 liters for 90 + 30 + 30 = 150 yen.

Sample Input 2

10000 1000 100 10
1

Sample Output 2

100

Even though a 2-liter bottle costs just 10 yen, you need only 1 liter.
Thus, you have to buy a 1-liter bottle for 100 yen.

Sample Input 3

10 100 1000 10000
1

Sample Output 3

40

Now it's better to buy four 0.25-liter bottles for 10 + 10 + 10 + 10 = 40 yen.

Sample Input 4

12345678 87654321 12345678 87654321
123456789

Sample Output 4

1524157763907942

Solution in JavaScript (node.js v5.12) (judge verdict: Runtime Error)

const rec = (db, N, price, f) => {
  if(db.length === 0){
    return
  } 
  const a = db.pop()
  const n = a.n
  const p = a.p
  for(; N>0; N-=n, price+=p){
    rec(db, N, price, f)
  }
  if(N === 0){
    f(price)
  }
}

const solve = input => {
  const z = input.split("\n").slice(0,2)
  const [Q, H, S, D] = z[0].split(' ').slice(0, 4).map(s => parseInt(s))
  const N = parseInt(z[1])
  const db = [[0.25, Q], [0.5, H], [1, S], [2, D]].map(x => 0||{ n:x[0], p:x[1] })

  let pool = []
  rec(db, N, 0, p=>pool.push(p))
  console.log(Math.min(...pool))
}
//p=process.stdin;p.resume();p.setEncoding('utf8');p.on('data',x=>{ solve(x.toString())})