Taum is planning to celebrate the birthday of his friend, Diksha. There are two types of gifts that Diksha wants from Taum: one is black and the other is white. To make her happy, Taum has to buy $b$ black gifts and $w$ white gifts.

The cost of each black gift is $bc$ units.
The cost of every white gift is $wc$ units.
The cost to convert a black gift into white gift or vice versa is $z$ units.

Determine the minimum cost of Diksha's gifts.

Example

$b=3$

$w=5$

$bc=3$

$wc=4$

$z=1$

He can buy a black gift for $3$ and convert it to a white gift for $1$, making the total cost of each white gift $4$. That matches the cost of a white gift, so he can do that or just buy black gifts and white gifts. Either way, the overall cost is $3*3+5*4=29$.

Function Description

Complete the function taumBday in the editor below. It should return the minimal cost of obtaining the desired gifts.

taumBday has the following parameter(s):

int b: the number of black gifts
int w: the number of white gifts
int bc: the cost of a black gift
int wc: the cost of a white gift
int z: the cost to convert one color gift to the other color

Returns

int: the minimum cost to purchase the gifts

Input Format

The first line will contain an integer $t$, the number of test cases.

The next $t$ pairs of lines are as follows:

• The first line contains the values of integers $b$ and $w$.

• The next line contains the values of integers $bc$, $wc$, and $z$.

Constraints

$1\leq t\leq10$

$0\leq b,w,bc,wc,z\leq10^9$

Output Format

$t$ lines, each containing an integer: the minimum amount of units Taum needs to spend on gifts.

Sample Input
STDIN Function
----- --------
5 t = 5
10 10 b = 10, w = 10
1 1 1 bc = 1, wc = 1, z = 1
5 9 b = 5, w = 5
2 3 4 bc = 2, wc = 3, z = 4
3 6 b = 3, w = 6
9 1 1 bc = 9, wc = 1, z = 1
7 7 b = 7, w = 7
4 2 1 bc = 4, wc = 2, z = 1
3 3 b = 3, w = 3
1 9 2 bc = 1, wc = 9, z = 2

Sample Output
20
37
12
35
12

Explanation

Test Case #01:

Since black gifts cost the same as white, there is no benefit to converting the gifts. Taum will have to buy each gift for 1 unit. The cost of buying all gifts will be: $b*bc+w*wc=10*1+10*1=20$.

Test Case #02:

Again, he cannot decrease the cost of black or white gifts by converting colors. $z$ is too high. He will buy gifts at their original prices, so the cost of buying all gifts will be: $b*bc+w*wc=5*2+9*3=10+27=37$.

Test Case #03:

Since $bc > wc +z$, he will buy $b+w=3+6=9$ white gifts at their original price of $1$. $b=3$ of the gifts must be black, and the cost per conversion, $z=1$. Total cost is $9*1+3*1=12$.

Test Case #04:

Similarly, he will buy $w=7$ white gifts at their original price, $wc=2$. For black gifts, he will first buy white ones and color them to black, so that their cost will be reduced to $wc+z=2+1=3$. So cost of buying all gifts will be: $7*3+7*2=35$.

Test Case #05:
He will buy black gifts at their original price, $bc=1$. For white gifts, he will first black gifts worth $bc=1$ unit and color them to white for $z=2$ units. The cost for white gifts is reduced to $wc=b c+z=2+1=3$ units. The cost of buying all gifts will be: $3*1+3*3=3+9=12$.

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