PHP/MySQL Login Form

<?php

$host = "localhost";
$user = "root";
$pass = "";
$db = "fast";

mysql_connect($host, $user, $pass);
mysql_select_db($db);

    if (isset ($_POST['username'])) {
        $username = $_POST['username'];
        $password = $_POST['password'];
    $sql = "SELECT * FROM users WHERE username='".$username."' AND password='".$password."' LIMIT 1";
    $res = mysql_query($sql);
    if (mysqli_num_rows($res) == 1) {
        echo "You have succesfully logged in.";
        exit();
    } else {
        echo "Invalid login information. Please return the previous page";
        exit();
    }
}

?>


<!DOCTYPE html>
<html>
<head>
    <title>Login</title>
</head>

<body>
    <form method="POST" action="login.php">
        Username: <input type="text" name="username"></input>
        Password: <input type="password" name="password"></input>
        <input type="submit" name="submit" value="Log In"></input>
    </form>
</body>
</html>