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Time Limit: 5000 MS    Memory Limit: 131072 K

Description

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.

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. InitiallyWormly¡¯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 animationWormly¡¯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 takesWormly to cross Bridgely.
If it is impossible to get across while satisfying the constraints, the line must contain

Sample Input

3
1 2 2
11
2 3 5
11011
1 3 5
11011

Sample Output

1
IMPOSSIBLE
5

Source
NWERC 2010

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