FIRST_VALUE() does not preserve the exact data type

CREATE OR REPLACE TABLE t1 (a INT, b INT, c FLOAT);

INSERT INTO t1 VALUES (1,1,1),(1,2,2),(2,1,1),(2,2,2);

CREATE OR REPLACE TABLE t2 AS SELECT a, FIRST_VALUE(b) OVER(), FIRST_VALUE(c) OVER() FROM t1 GROUP BY a;

SHOW CREATE TABLE t2;

+-------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+

| Table | Create Table                                                                                                                                                                            |

+-------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+

| t2    | CREATE TABLE `t2` (

  `a` int(11) DEFAULT NULL,

  `FIRST_VALUE(b) OVER()` bigint(11) DEFAULT NULL,

  `FIRST_VALUE(c) OVER()` double DEFAULT NULL

) ENGINE=InnoDB DEFAULT CHARSET=latin1 |

+-------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+