Draw a game tree that accurately represents the following strategic situation:

Two states, A and B, are engaged in an arms race.

State A moves first and has the option to sign an arms control treaty (S) or not (S).

B observes A's choice of whether or not to sign, and following either, may itself choose whether or not to sign (s) or (s).

Following B's decision to sign, the game ends if at least one side signed the treaty.

-If both signed, each receives 3 utility.

-If one state signs and the other does not, the non-signer gets 5 while the signer gets 0.

If both sides choose not to sign the treaty, the game does not end. Instead, the arms race continues, and A begins by having the option to either expand their arsenal (E) or not (E). This move occurs in secret and is not observed by B. After A's expansion decision, B may also choose whether or not to expand their own arsenal (e) or (e), and the game ends. During the arms race, if both states do not expand, each receives 4 utility. If both expand, each receives 2. If one expands while the other does not, the state that expands receives 6 utility and the other 1.