constant "Lead" {
EcFixedPointShort VALUE_COMMIT_VALUE,
EcFixedPoint VALUE_COMMIT_RANDOM,
EcFixedPointBase NULLIFIER_K,
}

contract "Lead" {
MerklePath c1_cm_path,
Uint32 c1_cm_pos,
Unit32 c1_sk_pos,
Base c1_sk,
Base c1_sk_root,
MerklePath c1_sk_path,
Base c1_tau,
Base c1_rho,
Scalar c1_opening,
Base value,
Scalar c2_opening,
Scalar rho_opening,
Scalar y_opening,
Base sigam1,
Base sigma2
}

circuit "Lead" {
ONE = witness_base(2);
ZERO = witness_base(0);
PREFIX_EVL = witness_base(2);
PREFIX_SEED = witness_base(3);
PREFIX_CM = witness_base(4);
PREFIX_PK = witness_base(5);

# coin (1) pk
pk = poseidon_hash(PREFIX_PK, c1_sk_root, c1_tau, ZERO);
constrain_instance(pk);
# coin (2) rho/nonce 
c2_rho = poseidon_hash(PREFIX_EVL, c1_sk_root, c1_rho, ZERO);
constrain_instance(c2_rho);
# coin (1) cm/commitment
c1_cm_msg = poseidon_hash(PREFIX_CM, pk, value, c1_rho);
c1_cm_v = ec_mul_short(c1_cm_msg, VALUE_COMMIT_VALUE);
c1_cm_r = ec_mul(c1_opening, VALUE_COMMIT_RANDOM);
c1_cm = ec_add(c1_cm_v, c1_cm_r);
c1_cm_x = ec_get_x(c1_cm);
c1_cm_y = ec_get_y(c1_cm);
constrain_instance(c1_cm_x);
constrain_instance(c1_cm_y);
# coin (2) cm/commitment
c2_cm_msg = poseidon_hash(PREFIX_CM, pk, value, c2_rho);
c2_cm_v = ec_mul_short(c2_cm_msg, VALUE_COMMIT_VALUE);
c2_cm_r = ec_mul(c2_opening, VALUE_COMMIT_RANDOM);
c2_cm = ec_add(c2_cm_v, c2_cm_r);
c2_cm_x = ec_get_x(c2_cm);
c2_cm_y = ec_get_y(c2_cm);
constrain_instance(c2_cm_x);
constrain_instance(c2_cm_y);
# root of path to burnt coin commitment at given pos
root = merkle_root(c1_cm_pos, c1_cm_path, c1_cm);
constrain_instance(root);
# root of path at c1_sk_pos
root_sk = merkle_root(c1_sk_pos, c1_sk_path, c1_sk);
constrain_instance(root_sk);
# coin (1) sn/nullifier
sn = poseidon_hash(PREFIX_SN, c1_sk_root, c1_rho, ZERO);
constrain_instance(sn);
# lottery seed
seed = poseidon_hash(PREFIX_SEED, c1_sk_root, c1_rho, ZERO);
# y
y_v = ec_mul_short(seed, VALUE_COMMIT_VALUE);
y_r = ec_mul(y_opening, VALUE_COMMIT_RANDOM);
y = ec_add(y_v, y_r);
y_x = ec_get_x(y);
y_y = ec_get_y(y);
constrain_instance(y_x);
constrain_instance(y_y);
# rho
rho_v = ec_mul_short(seed, VALUE_COMMIT_VALUE);
rho_r = ec_mul(rho_opening, VALUE_COMMIT_RANDOM);
rho = ec_add(rho_v, rho_r);
rho_x = ec_get_x(rho);
rho_y = ec_get_y(rho);
constrain_instance(rho_x);
constrain_instance(rho_y);
# target
term1 = base_mul(sigma1, value);
term2_1 = base_mul(sigam2, value);
term2 = base_mul(term_2_1, value);
target = base_add(term1, term2);
# lottery
less_than(y, target)
}