# order of secp256k1 curve
ec_order = 0xfffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141


def drop_bytes_to_int(inp, n):
    """convert the int 'inp' to bytes (32), drop the first n bytes, return the corresponding int
    """
    return int.from_bytes((inp.to_bytes(32, "big")[n:]), "big")


# Step 1: P(n-th byte strictly below 0x80)
P1 = []
for i in range(32):
    P1 += [min(1, 2 ** (8 * (32 - i) - 1) / (drop_bytes_to_int(ec_order, i) - 1))]
# Step 2: P(n-th byte equal t0 0x00)
P2 = []
for i in range(32):
    P2 += [2 ** (8 * (32 - i - 1)) / (drop_bytes_to_int(ec_order, i) - 1)]
# Step 3: P(int encoded in n or less bytes), i.e. cumulative distribution
P3 = [1]
for i in range(32):
    tot = 1
    for j in range(i):
        tot *= P2[j]
    P3 += [P1[i] * tot]
P3 += [0]
# Step 4: P(int encoded in n bytes)
P4 = []
for i in range(33):
    P4 += [P3[i] - P3[i + 1]]
# Step 5: P(signature encoded in n bytes)
P5 = []
for i in range(66):
    tot = 0
    for j in range(i + 1):
        tot += (0 if j > 32 else P4[j]) * (0 if i - j < 0 or i - j > 32 else P4[i - j])
P5 += [tot]