Logs Stacking
Time Limit:2000MS Memory Limit:65536K
Total Submit:768 Accepted:234
Description Daxinganling
produces a lot of timber. Before loading onto trains, the timberjacks
will place the logs to some place in the open air first. Looking from
the sideway, the figure of a logs stack is as follows:
We have known that the number of logs in each layer is fewer
than the lower layer for at least one log, and that in each layer the
logs are connected in a line. In the figure above, there are 12 logs in
the bottom layer of the stack. Now, given the number of logs in the
bottom layer, the timberjacks want to know how many possible figures
there may be.
Input The
first line of input contains the number of test cases T (1 <= T
<= 1000000). Then T lines follow. Every line only contains a number
n (1 <= n <= 2000000000) representing the number of logs in the
bottom layer.
Output For
each test case in the input, you should output the corresponding number
of possible figures. Because the number may be very large, just output
the number mod 10^5.
Sample Input
4
1
2
3
5
Sample Output
1
2
5
34
Source POJ Monthly--2006.01.22,anonymous
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