Algorithm title: UVA 10564 Paths through the Hourglass (DP)

In the hourglass to the right a path is marked. A path always starts at the "the" and ends at the last row. Each cell in the path (except the "should") is directly below to the left or right of the cell in the path in the Prev IOUs row. The value of a path is the sum of the values in the path.

A path is described with an integer representing the starting point in the "the leftmost cell being 0) followed by a direction string containing the letters L and R, telling whether to go to the left or righ T. For instance, the ' path to the ' right ' is described as 2 rrrllrrrlr.

Given the values of each cell in a hourglass as as as as as as an integer S, calculate the number of distinct paths wit H value S. If at least one pathexist, your should also print the path with the lowest starting point. If Several such paths exist, select the one which has the lexicographically smallest the direction string.

Input

The input contains several cases. Each case starts with a line containing two integers N and S (2≤n≤20, 0≤s<500), the number of cells I n the the hourglass and the desired sum. Next follows 2n-1 lines describing each row in the hourglass. Each line contains a space separated list of integers between 0 and 9 inclusive. The A These lines would contain N integers, then N-1, ..., 2, 1, 2, ..., N-1, n.

The input would terminate with n=s=0. This case should is processed. There is less than cases in the input.

Output

For each case, the number of distinct paths. If at least one path exist, output in the next line the description of the path mentioned above. If no path exist, output a blank line instead.

Sample input Output for sample input