Implement a Rate Limiter

Rate-limit requests by key. The original problem allows fixed-window or sliding-window, requiring only consistency with the examples; this site explicitly uses a fixed window: the window number is floor(timestamp/window), and each key may have at most limit requests allowed within one window number. Rejected requests do not consume quota.

输入格式

The first line contains window limit q; then q lines of timestamp key. Added by this site: timestamp is a non-negative integer and non-decreasing, and key contains no spaces; 1≤q≤200000, 1≤window≤10^9, 1≤limit≤10^5.

输出格式

For each request, output ALLOW or REJECT, separated by spaces.

样例 1

输入：

10 2 6
1 alice
2 alice
3 alice
11 alice
12 alice
12 bob

输出：

ALLOW ALLOW REJECT ALLOW ALLOW ALLOW

样例 2

输入：

5 1 5
1 u
1 u
2 u
6 u
6 u

输出：

ALLOW REJECT REJECT ALLOW REJECT

样例 3

输入：

3 2 4
0 x
1 x
2 x
3 x

输出：

ALLOW ALLOW REJECT ALLOW