MySQL 8.0

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CREATE TABLE prof(id BIGINT, name varchar(10));
CREATE TABLE user(id BIGINT, name varchar(10))
CREATE TABLE login(id BIGINT, name varchar(10))
CREATE TRIGGER before_prof_insert
BEFORE INSERT
ON prof FOR EACH ROW
BEGIN
    DECLARE prof_ BIGINT;
    DECLARE user_ BIGINT;
    DECLARE res_ BIGINT;
    SELECT MAX(id) into prof_ FROm prof;
    SELECT MAX(id) into user_ FROm user;
    
    IF user_ IS NULL AND @prof IS NULL THEN
        SET res_ := 1;
    ELSE
        IF user_ > prof_  THEN
            SET res_ := user_ + 1;
        ELSE
            SET res_ := prof_ + 1;
        END IF;
    END if;
    SET NEW.id = res_;
    
    INSERT INTO login VALUES (res_,NEW.name);

END
CREATE TRIGGER before_user_insert
BEFORE INSERT
ON user FOR EACH ROW
BEGIN
    DECLARE prof_ BIGINT;
    DECLARE user_ BIGINT;
    DECLARE res_ BIGINT;
    SELECT MAX(id) into prof_ FROm prof;
    SELECT MAX(id) into user_ FROm user;
    
    IF user_ IS NULL AND prof_ IS NULL THEN
        SET res_ := 1;
    ELSE
        IF user_ > prof_  THEN
            SET res_ := user_ + 1;
        ELSE
            SET res_ := prof_ + 1;
        END IF;
    END if;
    SET NEW.id = res_;
    
    INSERT INTO login VALUES (res_,NEW.name);

END
INSERT INTO prof VALUES (0,'profa');)
INSERT INTO user VALUES (0,'usera');
INSERT INTO prof VALUES (0,'profb');
INSERT INTO prof VALUES (0,'profc');
INSERT INTO user VALUES (0,'userb');
INSERT INTO prof VALUES (0,'profd');
SELECT * FROM prof;


id
name


1
profa

3
profb

4
profc

6
profd


SELECT * FROM user;


id
name


2
usera

5
userb


SELECT * FROM login;


id
name


1
profa

2
usera

3
profb

4
profc

5
userb

6
profd