Jonly is writing his first computer game. For the opening scene he
wants to have the main character, Wormly, cross Bridgely, the
bridge. Wormly is a worm made of b equal circular bubbles and L
legs. At all times each leg has to be under one of the bubbles, and
under each bubble there can be at most one leg. Bridgely was supposed
to be composed of n planks with the width of each plank equal to the
diameter of each of Wormly's bubbles. However, some of the planks are
missing.
At every moment, Wormly can do exactly one of the following:
Move one of its legs forward over any number of (possibly
missing) planks. After the move, the leg should be on a plank and
underneath one of Wormly's bubbles. A leg isn't allowed to overtake other legs.
Move all of its bubbles forward one plank while its legs remain on
the same planks. After the move each leg must still be under one of
Wormly's bubbles.
Figure 1: In this example, the only possible move for the last leg is to position b.
(The plank at position a is missing, so the leg cannot move there.
To get to position c, the last leg would have to overtake the first leg.)
Also, in this example, moving all the bubbles forward is not allowed because Wormly's last leg would end up without a bubble over it.
Now Jonly is wondering how long the animation takes until Wormly
reaches the end of Bridgely. Initially Wormly's bubbles are directly above the
leftmost b planks of the bridge and its legs are on the leftmost L
planks. At the end of the animation Wormly's bubbles have to be directly above
the rightmost b planks and its legs have to be on the rightmost L
planks.
The left- and rightmost L planks of Bridgely are not missing.
Input
On the first line a positive integer: the number of test cases, at
most 100. After that per test case:
One line with three integers L, b and n (1 ≤ L ≤ b ≤ n ≤ 1 000 000): the number of legs, the number of bubbles and the
length of the bridge respectively.
One line with a string consisting of n characters, either `0' or `1', describing
Bridgely. A one indicates a plank and a zero indicates a missing
plank.
Output
Per test case:
One line with an integer: the minimum number of steps it takes
Wormly to cross Bridgely. If it is impossible to get across
while satisfying the constraints, the line must contain
"IMPOSSIBLE" instead.
