Sum of Substrings

1000ms

262144K

Description:

You are given a binary string $$$s$$$ of length $$$n$$$.

Let's define $$$d_i$$$ as the number whose decimal representation is $$$s_i s_{i+1}$$$ (possibly, with a leading zero). We define $$$f(s)$$$ to be the sum of all the valid $$$d_i$$$. In other words, $$$f(s) = \sum\limits_{i=1}^{n-1} d_i$$$.

For example, for the string $$$s = 1011$$$:

$$$d_1 = 10$$$ (ten);
$$$d_2 = 01$$$ (one)
$$$d_3 = 11$$$ (eleven);
$$$f(s) = 10 + 01 + 11 = 22$$$.

In one operation you can swap any two adjacent elements of the string. Find the minimum value of $$$f(s)$$$ that can be achieved if at most $$$k$$$ operations are allowed.

Input:

Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 10^5$$$). Description of the test cases follows.

First line of each test case contains two integers $$$n$$$ and $$$k$$$ ($$$2 \le n \le 10^5$$$, $$$0 \le k \le 10^9$$$) — the length of the string and the maximum number of operations allowed.

The second line of each test case contains the binary string $$$s$$$ of length $$$n$$$, consisting of only zeros and ones.

It is also given that sum of $$$n$$$ over all the test cases doesn't exceed $$$10^5$$$.

Output:

For each test case, print the minimum value of $$$f(s)$$$ you can obtain with at most $$$k$$$ operations.

Sample Input:

Sample Output:

21
22
12

Note:

For the first example, you can't do any operation so the optimal string is $$$s$$$ itself. $$$f(s) = f(1010) = 10 + 01 + 10 = 21$$$.
For the second example, one of the optimal strings you can obtain is "0011000". The string has an $$$f$$$ value of $$$22$$$.
For the third example, one of the optimal strings you can obtain is "00011". The string has an $$$f$$$ value of $$$12$$$.

Informação

Provedor Codeforces

Código CF1691C