Задача на сближение

def min_meeting_time(S, Z, M):
 
 
    min_time = float('inf')
 
    for z_jumps in range(S // Z + 1):
        remaining_distance = S - z_jumps * Z
        if remaining_distance % M == 0:
            m_jumps = remaining_distance // M
            total_time = max(z_jumps, m_jumps)
            min_time = min(min_time, total_time)
 
    return min_time if min_time != float('inf') else -1
 
 
S = int(input())
Z = int(input())
M = int(input())
 
result = min_meeting_time(S, Z, M)
print(result)

k=10000000000
s=int(input())
z=int(input())
m=int(input())
for i in range(0,s+1):
    for j in range(0,s+1):
        if s==z*i+m*j:
            k=min(i+j,k)                  
if k==10000000000:
    print(-1)
else:
    print(k)

k=10000000000
s=int(input())
z=int(input())
m=int(input())
for i in range(0,s+1):
    for j in range(0,s+1):
        if s==z*i+m*j:
            k=min(max(i,j),k)                  
if k==10000000000:
    print(-1)
else:
    print(k)

s = 7
m = 2
z = 3
vJumps = [m, z, m + z]
dp = [float('inf')] * (s + 1)
dp[0] = 0
 
for i in range(len(dp)):
    if dp[i] != float('inf'):
        for jLen in vJumps:
            if i + jLen < len(dp):
                dp[i + jLen] = min(dp[i + jLen], dp[i] + 1)
 
print(-1 if dp[-1] == float('inf') else dp[-1])

def gcd_ext(a, b):
    if b == 0:
        return a, 1, 0
    d, x, y = gcd_ext(b, a % b)
    x, y = y, x - (a//b) * y
    return d, x, y
 
 
z = 2
m = 17
s = 10**10 
d, x, y = gcd_ext(m, z)
res = -1
if s % d == 0:
    k = s // d
    t = k*x // (z//d)
    x = k*x - (z//d) * t
    y = (s - m*x) // z
    
    step = abs(x - y) // (m + z)
    if x > y:
        x, y = y, x 
        m, z = z, m 
    x += z * step
    y -= m * step
    res = -1 if x < 0 else max(x, y)
    res = min(res, max(x + z, y - m))
    
print(res)