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.
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.
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.
5 795
307 0 154 334 0
4 1300
350 350 350 250
In sample 1, the schedule has attained its maximum number of Failed Predictions. In the constructed schedule,
In sample 2, it can be shown that it is impossible to construct a plan that contains any Failed Prediction. In the constructed schedule,