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Need help with menu/nested loop/switch?

aa3685 (2)
For class we are supposed to make a Menu using a while loop and a switch statement. I have done the given code, but the output keeps giving me an extra menuT. How do I fix this and make it look like the expected output? 

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  #include <iostream>
using namespace std;

int main()
{
    string menuT="\n==== Menu Top ====\nA\tGoTo Menu A\nB\tGoTo Menu B\nE\tExit: ";
    string menuA="\n\t==== Menu A ====\n\tA\tDo Action A\n\tB\tDo Action B\n\tE\tExit: ";
    string menuB="\n\t==== Menu B ====\n\tA\tDo Action A\n\tB\tDo Action B\n\tE\tExit: ";
    string mexit="Exit Menu";
    string badi ="Bad Input";
    string dida ="\tDid A";
    string didb ="\tDid B";

    char c;
    while(c == 'a' || 'b' || 'e')
    {
        cout << menuT;
        cin >> c;

        switch (c)
        {
            case 'a':
                    cout << menuA;
                    cin >> c;
                        if (c == 'a')
                            cout << dida << menuA;
                        else if (c == 'b')
                            cout << didb << menuA;
                        else if (c == 'e')
                            cout << mexit << menuT;
                        else
                            cout << badi;
                        break;
            case 'b':
                    cout << menuB;
                    cin >> c;
                        if (c == 'b')
                            cout << didb << menuB;
                        else if (c == 'a')
                            cout << dida << menuB;
                        else if (c == 'e')
                            cout << mexit << menuT;
                        else
                            cout << badi;
                    break;
            default :
                cout << badi;

                }
    }
    return 0;


Here is the expected output:
==== Menu Top ====
A       GoTo Menu A
B       GoTo Menu B
E       Exit: 2
Bad Input

==== Menu Top ====
A       GoTo Menu A
B       GoTo Menu B
E       Exit: a
        ==== Menu A ====
        A       Do Action A
        B       Do Action B
        E       Exit: 2
        Bad Input

        ==== Menu A ====
        A       Do Action A
        B       Do Action B
        E       Exit: e
        Exit Menu

==== Menu Top ====
A       GoTo Menu A
B       GoTo Menu B
E       Exit: b

        ==== Menu B ====
        A       Do Action A
        B       Do Action B
        E       Exit: 2
        Bad Input

        ==== Menu B ====
        A       Do Action A
        B       Do Action B
        E       Exit: a
        Did A

        ==== Menu B ====
        A       Do Action A
        B       Do Action B
        E       Exit: b
        Did B

        ==== Menu B ====
        A       Do Action A
        B       Do Action B
        E       Exit: e
        Exit Menu

==== Menu Top ====
A       GoTo Menu A
B       GoTo Menu B
E       Exit: e
Exit Menu
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