# | Problem | Pass Rate (passed user / total user) |
---|---|---|
11168 | circulant matrix |
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11593 | Mexican Wave |
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Description
A circulant matrix is a square matrix in which all column vectors are composed of the same elements and each column vector is rotated one element to the down relative to the preceding column vector.
Given a vector of dimension N, use it to create an N-by-N circulant matrix. An example of circulant matrix:
1 5 4 3 2
2 1 5 4 3
3 2 1 5 4
4 3 2 1 5
5 4 3 2 1
Input
The first line contains a positive integer N indicating the size of the matrix.
The second line contains N numbers indicating the components of the vector. Note that each component of the vector is a one-digit number.
Output
The N-by-N circulant matrix. Print the elements of the matrix using the format "%2d".
Each row is ended with a newline character '\n'.
Sample Input Download
Sample Output Download
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Description
James, a pro photographer, recently went to a baseball game. He was very interested in Mexican wave, so he decided to take some photos of it.
Image that there are n spectators in the stadium, labelled from 1 to n. The maximum length of the wave is m. The spectators start the Mexican wave at time 0.
- At time 1, the first spectator stands.
- At time 2, the second spectator stands.
- ...
- At time m, the m-th spectator stands.
- At time m + 1, the (m + 1)-th spectator stands and the first spectator sits.
- At time m + 2, the (m + 2)-th spectator stands and the second spectator sits.
- ...
- At time n, the n-th spectator stands and the (n - m)-th spectator sits.
- At time n + 1, the (n + 1 - m)-th spectator sits.
- ...
- At time n + m, the n-th spectator sits.
Now, James prints out T pictures he took and wants to play a game with you. For each picture, James will give you n, m, and the time t he took the picture. Can you predict how will picture looks like?
If you win the game, maybe James will teach you some tips about shooting an astonishing picture.
Input
The first line contains one integer number T, representing the numbers of photos.
The next T lines contain three integers n, m, t, representing the number of spectators, the maximum length of the wave, and the time James took the picture.
1 <= T <= 100
1 <= m <= n <= 100
0 <= t <= 100
Output
For each picture please output a line contains n characters, representing the states of the n spectators. If a spectator is sitting, please print '-', otherwise please print '^'. You can find out more information in sample output.