How to set parameters (i.e., gen, ords and mvec) for bootstrapping in HElib?

I'm using the homomorphic encryption library, HElib, to do experiments. I tried to use bootstrapping with parameters that are not in the table provided with HElib. But I have no idea how to choose the parameters (i.e, gen, ords and mvec) for bootstrapping.

Below is an example in HElib (examples/BGV_binary_arithmetic.cpp)

  // Plaintext prime modulus.
  long p = 2;
  // Cyclotomic polynomial - defines phi(m).
  long m = 4095;
  // Hensel lifting (default = 1).
  long r = 1;
  // Number of bits of the modulus chain.
  long bits = 500;
  // Number of columns of Key-Switching matrix (typically 2 or 3).
  long c = 2;
  // Factorisation of m required for bootstrapping.
  std::vector<long> mvec = {7, 5, 9, 13};
  // Generating set of Zm* group.
  std::vector<long> gens = {2341, 3277, 911};
  // Orders of the previous generators.
  std::vector<long> ords = {6, 4, 6};

My question: In my experiment, I need the ciphertext with the exact number of slots (such as slots= 256, 1024, 4096). Thus, I have to find the proper m, p, bits to generate such a ciphertext with these slots. But for these m, p, bits, I don't know how to set mvec, gens, ords.

Here is a particular example:

    long m = 12800;
    long p = 127;
    long r = 1;
    long bits = 119;
    long c = 2;
    vector<long> mvec = {25, 512};
    vector<long> gens = {2, 128};
    vector<long> ords = {43, 4351};

Throw an exception: terminating with uncaught exception of type helib::LogicError: Bad user-supplied generator

// Some Information about this context:
m = 12800, p = 127, phi(m) = 5120
  ord(p) = 20
  normBnd = 1.23107
  polyNormBnd = 1.23107
  factors = [2 5]
  generator 43 has order (== Z_m^*) of 128
  generator 4351 has order (== Z_m^*) of 2
r = 1
nslots = 256
hwt = 0
ctxtPrimes = [6,7]
specialPrimes = [8]
number of bits = 173

security level = 98.4643

Update: I run an example with the parameters found by HElib (misc/psi/params.cpp), but throw an exception LogicError: rawModSwitch scaled noise exceeds bound: 309684.692524.

The given parameters are: phim=7056, d=28, m=12789, m=(3^2)*7^2*{29}, m/phim(m)=1.81, C=74 D=2 E=2, mvec="[49 261]" gens="[11224 7106]" ords="[42 6]"

The code is written for performing multiple multiplications while checking the noise and performing bootstrapping.

    long m = 12789;
    long p = 127;
    long r = 1;
    long bits = 119;
    long c = 2;
    // Factorisation of m required for bootstrapping.
    vector<long> mvec = {49, 261};
    // Generating set of Zm* group.
    vector<long> gens = {11224, 7106};
    // Orders of the previous generators.
    vector<long> ords = {42, 6};
    
    Context context = ContextBuilder<BGV>()
                                   .m(m)
                                   .p(p)
                                   .r(r)
                                   .gens(gens)
                                   .ords(ords)
                                   .bits(bits)
                                   .c(c)
                                   .bootstrappable(true)
                                   .mvec(mvec)
                                   .build();
    // Key management
    SecKey secret_key(context);
    secret_key.GenSecKey();
    addSome1DMatrices(secret_key);
    addFrbMatrices(secret_key);
    secret_key.genRecryptData();
    const PubKey& public_key = secret_key;
    const EncryptedArray& ea = context.getEA();

    // create a ciphertext
    std::vector<long> ptxt(nslots);
    for (int i = 0; i < nslots; ++i) {
        ptxt[i] = 2;
    }
    Ctxt ctxt(public_key);
    ea.encrypt(ctxt, public_key, ptxt);

    // multiplication and bootstrapping
    for (int i = 0; i < 10; i++) {
        if (ctxt.bitCapacity() <= 50)
        {
            cout << "Begin bootstrapping!" << endl;
            public_key.thinReCrypt(ctxt);
        }
        ctxt.square();
    }

The exception:

Begin bootstrapping!
libc++abi: terminating with uncaught exception of type helib::LogicError: rawModSwitch scaled noise exceeds bound: 309684.692524
terminating with uncaught exception of type helib::LogicError: rawModSwitch scaled noise exceeds bound: 309684.692524