A. Advanced Preparations
time limit per test
0.5 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

The city of Aetherrain is notorious for its unpredictable weather. To protect students from dangerous floods, the mayor has announced:

"If the rainfall of any day is higher than or equal to 200 mm, classes the next day are suspended!"

Importantly, if classes are suspended and that day's rainfall is also $$$\geq 200$$$ mm, then the next day's classes are suspended too.

When classes were suspended but the day had $$$0$$$ mm rainfall, it's a Failed Prediction — angry parents complain about taking a day off for nothing while still paying school fees.

You, as a Raincaller, want to create as much chaos as possible. Your task is to plan a rainfall schedule that maximizes the number of days of Failed Predictions for the next $$$N$$$ days with a total rainfall of exactly $$$S$$$ mm, and the amount of rainfall on each day must be a non-negative integer. To avoid severe flooding, the rainfall on a single day should not exceed $$$350$$$ mm.

Any schedule that maximizes the number of Failed Predictions would be accepted.

Input

The first line contains two integers $$$N$$$ $$$(1 \le N \le 100)$$$ and $$$S$$$ $$$(0 \le S \le 350\cdot N)$$$, representing the number of days and the total rainfall of the $$$N$$$ days respectively.

Output

The output only contains one line, a construction of rainfall for the next $$$N$$$ days that attains this maximum value, where the $$$i$$$-th integer represents the amount of rainfall on day $$$i$$$. If there are multiple solutions, output any of them.

Examples
Input
5 795
Output
307 0 154 334 0
Input
4 1300
Output
350 350 350 250
Note

In sample 1, the schedule has attained its maximum number of Failed Predictions. In the constructed schedule,

  • On day $$$1$$$, the rainfall is $$$307$$$ $$$(\geq 200)$$$ mm. The classes on day $$$2$$$ are suspended.
  • On day $$$2$$$, the rainfall is $$$0$$$ mm. The classes are suspended but the rainfall is $$$0$$$ mm. Thus, a Failed Prediction is recorded.
  • On day $$$3$$$, the rainfall is $$$154$$$ $$$( \lt 200)$$$ mm. Therefore, the classes on day $$$4$$$ are not suspended.
  • On day $$$4$$$, the rainfall is $$$334$$$ $$$(\geq 200)$$$ mm. The classes on day $$$5$$$ are suspended.
  • On day $$$5$$$, the rainfall is $$$0$$$ mm. The classes are suspended but the rainfall is $$$0$$$ mm. Thus, another Failed Prediction is recorded.

In sample 2, it can be shown that it is impossible to construct a plan that contains any Failed Prediction. In the constructed schedule,

  • On days $$$1$$$ to $$$3$$$, the rainfall is $$$350$$$ mm each day. The amount of rainfall must not exceed $$$350$$$ mm, as it would cause city flooding.
  • On day $$$4$$$, the rainfall is $$$250$$$ $$$(\geq 200)$$$ mm. However, since day 5 is out of the schedule, no further Failed Predictions can occur.