Wrong result for CAST(AVG(bigint_column) AS SIGNED)

DROP TABLE IF EXISTS t1;

CREATE TABLE t1 (id INT, a BIGINT);

INSERT INTO t1 VALUES (1,0x7FFFFFFFFFFFFFFF),(2,0x7FFFFFFFFFFFFFFF);

SELECT id, AVG(a) AS avg, CAST(MIN(a) AS SIGNED) AS cast_min FROM t1 GROUP BY id HAVING avg!=123 ORDER BY id;

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

| id   | avg                      | cast_min            |

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

|    1 | 9223372036854775807.0000 | 9223372036854775807 |

|    2 | 9223372036854775807.0000 | 9223372036854775807 |

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

SELECT id, AVG(a) AS avg, CAST(AVG(a) AS SIGNED) AS cast_avg FROM t1 GROUP BY id HAVING avg!=123 ORDER BY id;

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

| id   | avg                      | cast_avg             |

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

|    1 | 9223372036854775807.0000 | -9223372036854775808 |

|    2 | 9223372036854775807.0000 | -9223372036854775808 |

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