Red‐Blue Interval Game

You are given an array \(a\) of \(n\) non‐negative integers. Initially, each element is colored blue. Two players, youyou and yy, play a game on a subarray of \(a\) in alternating turns; youyou moves first.

The game is defined as follows. Suppose the current subarray (game board) has indices \(L\) to \(R\):

• If it is youyou's turn, he may choose any contiguous interval of length at most \(c_1\). If the sum of the numbers in that interval is at most \(w_1\) (i.e. \(\sum_{i}\,a_i \le w_1\)), then he colors all numbers in that interval red.
• If it is yy's turn, he may choose any contiguous interval of length at most \(c_2\). If the sum of the numbers in that interval is greater than \(w_2\) (i.e. \(\sum_{i}\,a_i > w_2\)), then he colors all numbers in that interval blue.

If the current player has no valid interval to operate on, he skips his turn. The win conditions are as follows:

• youyou wins if at any moment the entire board (i.e. all numbers in the subarray) is red.
• yy wins if within \(10^{51971}\) turns youyou is unable to achieve an all‐red board.

Both players play optimally. In order to increase the challenge, the following \(q\) operations are performed on the array:

• If an operation is of the form 1 x y, then increase \(a_x\) by \(y\) (\(0 \le y \le 10^9\)).
• If an operation is of the form 2 x y, then consider the subarray \(a_x, a_{x+1}, \ldots, a_y\) and imagine a game played on this subarray with the rules described above. Output cont if youyou can force a win; otherwise, output tetris.

Important note on strategy: If the entire subarray can be colored red in one move (i.e. its length is at most \(c_1\) and its sum is at most \(w_1\)), then youyou wins immediately. Otherwise, since after the first move the board is not completely red, yy will try to revert any progress using his move if a valid interval exists. Thus, youyou can only force a win through multiple moves if he can gradually cover the subarray with "safe" moves. A move is considered safe if it cannot be immediately undone by yy. In particular:

• If a safe move is taken on an interval of length \(L\) and if \(L \le c_2\) then its sum must be at most \(\min(w_1, w_2)\) (so that yy cannot find a subinterval of length \(\le c_2\) with sum greater than \(w_2\)).
• If \(L > c_2\) then yy cannot choose the entire interval (since his limit is \(c_2\)), and only the condition \(\sum \le w_1\) (for youyou's move) needs to be satisfied.

Thus, one may show that in this problem youyou can force a win on a given subarray if and only if either the subarray can be turned red in one move, or the subarray can be partitioned into intervals of lengths at most \(c_1\) such that for each interval, if its length \(L \le c_2\) then its sum is at most \(\min(w_1, w_2)\), and if \(L > c_2\) then its sum is at most \(w_1\).

You are to process the \(q\) operations in order and answer the queries.

inputFormat

The first line contains six integers \(n, q, c_1, w_1, c_2, w_2\) where \(n\) is the number of elements in the array and \(q\) is the number of operations.

The second line contains \(n\) non‐negative integers \(a_1, a_2, \ldots, a_n\) representing the initial array.

Each of the following \(q\) lines contains an operation in one of the following two formats:

• 1 x y: Increase \(a_x\) by \(y\) (\(0 \le y \le 10^9\)).
• 2 x y: Query whether youyou can force a win on the subarray \(a_x, a_{x+1}, \ldots, a_y\).

outputFormat

For each operation of type 2, output a single line containing either cont if youyou can force a win, or tetris otherwise.

sample

5 5 3 10 2 5
1 2 3 4 5
2 1 5
1 3 1
2 1 3
1 5 0
2 2 5

cont
cont
cont

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