For the following problem:

Please write the C++ code. Here is the source code:

#include

#include //gcd

#include

using namespace std;

int main() {

int e,n; cin>>e>>n; //first line input

int m; cin>>m; //second line input

vector v(m); //vector that holds secret msg

for(int i = 0; i

cin>>v[i];

}

//TODO: solve the secret message

bool isValid = true; //make it false when invalid

int p,q,phi,d; //do something and solve them

vector decrNums(m); //initialized to size m

vector decrMsg(m); //initialized to size m

//solve write your code here

//printing output

if(isValid) {

cout

//print out vector of decrypted numbers

for(int i = 0; i

cout

//print out actual decrypted messages (ABC...Z " . , ')

for(int i = 0; i

} else {

cout

}

}

Problem 2: Alice's RSA public key is P = (e,n) = (5, 901). Bob sends Alice the message by encoding it as follows. First he assigns numbers to characters: A is 3, B is 4, ..., Z is 28, a blank is 29, quotation marks: 30, a period: 31, a coma: 32, an apostrophe: 33. Then he uses RSA to encode each number separately. Bob's encoded message is: 030 673 332 785 171 589 782 171 828 589 785 568 782 785 713 782 813 785 123 589 828 673 589 487 589 785 813 890 243 813 785 733 243 813 890 589 733 243 813 673 422 769 785 673 769 785 769 673 733 171 828 589 291 785 673 813 785 673 769 785 782 713 828 482 785 123 589 422 243 500 769 589 785 813 890 589 482 785 568 782 785 713 782 813 785 549 589 243 828 673 367 589 785 890 782 587 785 422 782 733 171 828 673 422 243 813 589 568 785 828 673 332 589 785 673 769 777 030 Decode Bob's message. Notice that you don't have Bob's secret key, so you need to "break RSA to decrypt his message. For the solution, you need to provide the following: (a) Describe step by step how you arrived at the solution: find p and q, o(n) and d. (b) Show your work (the computation) for one number in the message. (c) To decode the remaining numbers, you need to write a program in C++, test it on Codeforces and upload to canvas. (d) Give the decoded message (in integers). (e) Give Bob's message in plaintext (also, what does it mean and who said it). Your program should : (i) Take three integers, e, n (the public key for RSA), and m (the number of characters in the message) as input to your program. Next, input the ciphertext. (ii) Test whether the public key is valid. If not, output a single line Public key is not valid! and quit the program. (iv) If the public key is valid, decode the message. (v) Output p and q, (n) and d. 1 (vi) On a new line, output the decoded message in integers. (vii) On a new line, output the decoded message in English. The characters should be all uppercase. You can assume that the numbers will be assigned to characters according to the mapping above: A is 3, B is 4