Lights Off

문제

Bessie wants to go to sleep, but the farm's lights are keeping her awake. How can she turn them off?

Bessie has two bit strings of length $NN$ ($2\le N\le 202\backslash le\; N\backslash le\; 20$), representing a sequence of lights and a sequence of switches, respectively. Each light is either on (1) or off (0). Each switch is either active (1) or inactive (0).

A *move* consists of the following sequence of operations:

1. Toggle exactly one switch (set it to active if it is inactive, or vice versa).
2. For each active switch, toggle the state of the corresponding light (turn it off if it is on, or vice versa).
3. Cyclically rotate the switches to the right by one. Specifically, if the bit string corresponding to the switches is initially $s_0{s}_1\dots s_{N-1}s\_0s\_1\backslash dots\; s\_\{N-1\}$ then it becomes $s_{N-1}{s}_0{s}_1\dots s_{N-2}s\_\{N-1\}s\_0s\_1\backslash dots\; s\_\{N-2\}$.

For $TT$ ($1\le T\le 2\cdot {10}^{5}1\backslash le\; T\backslash le\; 2\backslash cdot\; 10^5$) instances of the problem above, count the minimum number of moves required to turn all the lights off.

입력

First line contains $TT$ and $NN$.

Next $TT$ lines each contain a pair of length-$NN$ bit strings.

출력

For each pair, the minimum number of moves required to turn all the lights off.

4 3
000 101
101 100
110 000
111 000

0
1
3
2

1 10
1100010000 1000011000

2