Google Kickstart 2018, Round error in test case

I'm trying to solve the Scrambled Words problem in Google Kickstart 2018, Round A.

I'm having trouble generating the input string. Here are the directions they gave

The third line contains two lowercase English letters S₁ and S₂, and five integers N, A, B, C and D. S₁ and S₂ are the first two characters of the professor's string S, N is the length of S, and the other four integers are parameters that you should use to generate the characters of S, as follows:

First we define ord(c) as the decimal value of a character c and char(n) as the character value of a decimal n. For example, ord('a') = 97 and char(97) = 'a'. You can refer to ASCII table for other conversions.

Now, define x₁ = ord(S₁), x₂ = ord(S₂). Then, use the recurrence below to generate x_i for i = 3 to N:

• x_i = ( A * x_i-1 + B * x_i-2 + C ) modulo D.

We define S_i = char(97 + ( x_i modulo 26 )), for all i = 3 to N.

Using these directions for the test input,

1
5
axpaj apxaj dnrbt pjxdn abd
a a 50 1 1 1 30

The string that I am generating is

aapaapaapaapaapaapaapaapaapaapaapaapaapaapaapaapaa

But the string that is supposed to be generated is

aapxjdnrbtvldptfzbbdbbzxtndrvjblnzjfpvhdhhpxjdnrbt

Here is my code

    char S1, S2;
    long N, A, B, C, D;
    cin >> S1 >> S2 >> N >> A >> B >> C >> D;
    A %= D;
    B %= D;
    C %= D;

    vector<char> S;
    S.push_back(S1);
    S.push_back(S2);

    for (int i = 2; i < N; i++) {
      long xi1 = (long)S[i - 1];
      long xi2 = (long)S[i - 2];
      long xi = (A * xi1) % D;
      xi += ((B * xi2) % D);
      xi += C;
      xi %= D;
      xi %= 26;

      char Si = (char)(97 + xi);
      S.push_back(Si);
    }