Sales Tax

Albert noticed something new on a receipt while traveling in a new city. The currency there is the dollar, but the city also uses the cent (c), which is 1/100 of a dollar. So 100 cents equal 1 dollar, and no unit smaller than a cent is used. For example, a price of 4.30 means 4 dollars and 30 cents, and 5.00 can be read as 5 dollars, 500 cents, or 3 dollars and 200 cents.

The receipt lists the total paid for the $N$ items Albert bought, including sales tax. Let $P_i$ be the price of the $i$-th item. Item prices exclude tax. The final payment $X$ is the sum of the item prices plus tax equal to $F$% of that sum, where $F$ is known to be a non-negative integer. Part of the receipt is torn, so the cent digits of $X$ are not visible and only the dollar amount is known.

For example, let $N = 3$, $X = 13$, and $P = [2.00, 4.49, 3.51]$.

• If $F = 25$: the item total is 10 dollars, the tax is 25% of that, or 2.50, so the total payment is 12.50.
• If $F = 30$: the tax is 3.00, so the total payment is 13.00.
• If $F = 39$: the tax is 3.90, so the total payment is 13.90.
• If $F = 40$: the tax is 4.00, so the total payment is 14.00.

Since $X = 13$ here, the possible tax rate $F$ is at least 30 and less than 40.

Albert checked another receipt and found something new. As noted, no unit smaller than a cent is used, so if the tax has a fraction of a cent, each store may round it up or down to the nearest cent. The receipt does not say which rule the store used. For example, let $N = 3$, $X = 19$, and $P = [1.98, 9.99, 4.99]$.

• The item total is 16.96.
• If $F = 10$: the tax is 1.696. The last digit 6 is a tenth of a cent, so the tax may be rounded down to 1.69 or up to 1.70. The total is then 18.65 or 18.66. Since $X = 19$, a 10% tax cannot match this receipt.
• If $F = 12$: the tax is 2.0352, which rounds to 2.03 or 2.04. The total is 18.99 or 19.00, so this receipt is consistent with a 12% tax.
• If $F = 17$: the tax is 2.8834, which rounds to 2.88 or 2.89. The total is 19.84 or 19.85, so this receipt is consistent with a 17% tax.

In this example, the dollar part of the total matches the receipt for every $F$ from 12 to 17 inclusive.

Given $N$, $X$, and the prices $P$ from the receipt, find the minimum and maximum tax values that match the dollar amount of $X$.

The first line contains the number of test cases $T$.

The first line of each test case contains two integers $N$ and $X$. The next $N$ lines contain the item prices $P_i$ in order. Each price always has a decimal point and exactly two digits after it for cents.

For each test case, print the minimum and maximum tax values that match, separated by a space, on one line.

• $1 \le T \le 10$
• $1 \le N \le 10^5$
• $0 \le X \le 10^8$
• $0.01 \le P_i \le 9.99$ for every $i$ with $1 \le i \le N$
• The minimum and maximum tax values for every test case are guaranteed to be between 0 and $10^4$ inclusive.