Menu rendered inside a dropdown is not overflown properly in the second level

Aim: The menu(created using the recursive function) inside a dropdown, which has more than n items should overflow.
Issue: The list of items overflows in the second level(SubMenu component), but the third level(SubMenu within a SubMenu component) is rendered within the second level.

Preview

Menu rendered within a DropDown:

Overflow given to SubMenu:

Third level is rendered within the second level:

Where second level should have rendered with overflow:

Object Structure:

let obj = [{
  label: "Type1",
  value: 1
}, {
  label: "Type2",
  value: "Type2",
  children: [{
    label: "Type2SubType1",
    value: 2
  }, {
    label: "Type2SubType2",
    value: 3
  }, {
    label: "Type2SubType3",
    value: 4
  }, {
    label: "Type2SubType4",
    value: 5
  }, {
    label: "Type2SubType5",
    value: 6
  }, {
    label: "Type2SubType6",
    value: 7
  }, {
    label: "Type2SubType7",
    value: 8
  }, {
    label: "Type2SubType8",
    value: 9
  }, {
    label: "Type2SubType9",
    value: 10
  }, {
    label: "Type2SubType10",
    value: 11
  }, {
    label: "Type2SubType11",
    value: 12
  }, {
    label: "Type2SubType12",
    value: 13
  }]
}, {
  label: "Type3",
  value: "Type3",
  children: [{
    label: "Type3SubType1",
    value: 14
  }, {
    label: "Type3SubType2",
    value: "Type3SubType2",
    children: [{
        label: "Type3SubType2SubSubType1",
        value: 15
    }, {
        label: "Type3SubType2SubSubType2",
        value: 16
    }, {
        label: "Type3SubType2SubSubType3",
        value: 17
    }, {
        label: "Type3SubType2SubSubType4",
        value: 18
    }, {
        label: "Type3SubType2SubSubType5",
        value: 19
    }, {
        label: "Type3SubType2SubSubType6",
        value: 20
    }, {
        label: "Type3SubType2SubSubType7",
        value: 21
    }]
  }]
}]

Recursive Function:

const recursive = (items) => {
  return (items && items.length > 0 &&
    items.map(item => {
      if (item.children && item.children.length > 0) {
        return (
          <SubMenu
            key={item.label}
            title={item.label}
          >
            {recursive(item.children)}
          </SubMenu>
        );
      } else {
        return (
          <Menu.Item key={item.value}>
            {item.label}
          </Menu.Item>
        );
      }
    }))
};

and wrapping it up with;

<Dropdown trigger={['click']} overlay={
    <Menu triggerSubMenuAction={'click'} className="menu" mode="vertical">
      {recursive(obj)}
    </Menu>}>

Start by reproducing the nested recursive Menu/SubMenu example inside a Dropdown, then inspect how the second-level SubMenu applies overflow to its children. Done means a third-level SubMenu is rendered outside the second-level overflow region while long second-level item lists still overflow correctly.