Problem Description
Farmer John hasProblem Description
As a member of the International Rock-Skipping League, you travel to a different lake each week and compete in a rock-skipping contest. The goal is to throw a rock so that it skips as many times as possible; the exact rules for determining the winner are given below. To make the competitions interesting, the IRSL often chooses lakes with logs, sandbars, and other obstacles. You are provided with a side-view, water-level "map" of the lake as shown in the top line of the example below. (The numbers 0..29 below the map are just for reference.) A period (".") indicates clear water, where a rock will skip; any other character indicates some kind of obstacle that will stop a rock.
...=...**..#...@....:.:.:..=..
______________________________
11111111112222222222
012345678901234567890123456789
You stand at the left end of the lake. You can throw a rock so that it lands at any position in the lake, and then skips at any fixed interval thereafter. So a throw can be defined as a pair (i,d), where i ≥ 0 is the initial landing position and d > 0 is the distance between skips. Note that d must be positive. The count of a throw is the number of times that it skips on the water. The length is the position of its last contact with either the water or an obstacle. To rank two distinct throws, use the following criteria, in order, until a winner is determined: count (highest wins); length (greatest wins); initial position (greatest wins); distance between skips (smallest wins).
For the map shown above, throw (27,2) hits the obstacle at position 27; it has count 0 and length 27. Throw (16,1) skips at positions 16, 17, 18, and 19, then hits the obstacle at position 20; it has count 4 and length 20, so it beats throw (27,2). Throw (2,7) skips at positions 2, 9, 16, and 23, then skips over the lake; it has count 4 and length 23, so it beats throw (16,1). Throw (1,4) skips at positions 1, 5, 9, 13, 17, 21, 25, and 29, then skips over the lake; it has count 8 and distance 29, and is the best possible throw for this lake.
Input
The input consists of one or more lake maps, each 1–40 characters long and on a line by itself, followed by a line containing only "END" that signals the end of the input. Positions within a map are numbered starting with zero. Maps will only contain printable ASCII punctuation characters. A period indicates clear water and any other character indicates an obstacle.
Output
For each map, compute the best possible throw (i,d), then output a line containing i and d separated by one space.
Sample Input
...=...**..#...@....:.:.:..=..
.(+)
/^.
++&
END
Sample Output
1 4
0 3
3 1
4 1
been informed of the location of a fugitive cow and wants to catch her immediately. He starts at a point N (0 ≤ N ≤ 100,000) on a number line and the cow is at a point K (0 ≤ K ≤ 100,000) on the same number line. Farmer John has two modes of transportation: walking and teleporting.
- Walking: FJ can move from any point X to the points X - 1 or X + 1 in a single minute
- Teleporting: FJ can move from any point X to the point 2 × X in a single minute.
If the cow, unaware of its pursuit, does not move at all, how long does it take for Farmer John to retrieve it?
Input
Line 1: Two space-separated integers: N and K
Output
Line 1: The least amount of time, in minutes, it takes for Farmer John to catch the fugitive cow.
Sample Input
5 17
Sample Output
4
