Unable to insert valid value to TIMESTAMP column

Unable to insert some valid values to TIMESTAMP column.
Steps to reproduce the bug:

1. Create new database: `create database SANDBOX;`
2. Create new table: `create table test (id int primary key auto_increment, time timestamp not null);`
3. Insert new row: `insert into test (time) values ('1984-04-01 00:59:37');`
   Expected result:
   `Query OK, 1 row affected (X.XX sec)`
   Actual result:
   `ERROR 1292 (22007): Incorrect datetime value: '1984-04-01 00:59:37' for column 'time' at row 1`

Additional info:
Another one value that causes the error: '2000-03-26 02:15:36'.
But, if I try to insert, say, '1974-04-01 00:59:37' or '1994-04-01 00:59:37' or '2001-03-26 02:15:36', it inserts without any error.
The error also happens if I try to update columns to set these values.