Problem: It's a very unfortunate day for Volodya today. He got bad mark in algebra and was therefore forced to do some work in the kitchen, namely to cook borscht (traditional Russian soup). This should also improve his algebra skills.

According to the borscht recipe it consists of n ingredients that have to be mixed in proportion <image> litres (thus, there should be a1 ·x, ..., an ·x litres of corresponding ingredients mixed for some non-negative x). In the kitchen Volodya found out that he has b1, ..., bn litres of these ingredients at his disposal correspondingly. In order to correct his algebra mistakes he ought to cook as much soup as possible in a V litres volume pan (which means the amount of soup cooked can be between 0 and V litres). What is the volume of borscht Volodya will cook ultimately?

Input

The first line of the input contains two space-separated integers n and V (1 ≤ n ≤ 20, 1 ≤ V ≤ 10000). The next line contains n space-separated integers ai (1 ≤ ai ≤ 100). Finally, the last line contains n space-separated integers bi (0 ≤ bi ≤ 100).

Output

Your program should output just one real number — the volume of soup that Volodya will cook. Your answer must have a relative or absolute error less than 10 - 4.

Examples

Input

1 100
1
40


Output

40.0


Input

2 100
1 1
25 30


Output

50.0


Input

2 100
1 1
60 60


Output

100.0

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
namespace QoE_Library {
namespace QL_Bare_Minimum {
const double PI = 3.141592653589793238460;
const long double E = 2.7182818284590452353;
const long double pi = 10000 * acos(-1.0L);
inline void inpS(char *a) { scanf("%s", a); }
inline int inpLLI(long long int &lld) { return scanf("%lld", &lld); }
inline int inpULLI(unsigned long long int &ulli) {
  return scanf("%llu", &ulli);
}
inline int inpI() {
  int n = 0;
  int ch = getchar();
  int sign = 1;
  while (ch < '0' || ch > '9') {
    if (ch == '-') sign = -1;
    ch = getchar();
  }
  while (ch >= '0' && ch <= '9')
    n = (n << 3) + (n << 1) + ch - '0', ch = getchar();
  n = n * sign;
  return n;
}
inline void inpI2(int &a, int &b) {
  a = inpI();
  b = inpI();
}
inline void inpI3(int &a, int &b, int &c) {
  a = inpI();
  b = inpI();
  c = inpI();
}
inline double inpD() {
  double res = 0.0;
  char c;
  while (1) {
    c = getchar();
    if (c == ' ' || c == '\n')
      continue;
    else
      break;
  }
  res = c - '0';
  while (1) {
    c = getchar();
    if (c >= '0' && c <= '9')
      res = 10 * res + c - '0';
    else
      break;
  }
  if (c == '.') {
    double decimal = 0.0, divi = 1.0;
    while (1) {
      c = getchar();
      if (c >= '0' && c <= '9')
        decimal += (c - '0') / (divi *= 10.0);
      else
        break;
    }
    res += decimal;
  }
  return res;
}
inline void outpD(double N) {
  char buff[24], sz = 0;
  int integer = N;
  int decimal = (N - integer) * 10000000;
  int tmp = decimal;
  while (decimal) {
    buff[sz++] = '0' + decimal % 10;
    decimal /= 10;
  }
  for (int decimal2 = 1000000; decimal2 > tmp; decimal2 /= 10) {
    buff[sz++] = '0';
  }
  buff[sz++] = '.';
  if (integer == 0) buff[sz++] = '0';
  while (integer) {
    buff[sz++] = '0' + integer % 10;
    integer /= 10;
  }
  while (--sz >= 0) putchar(buff[sz]);
  putchar(10);
}
inline int outpULLI(unsigned long long int u) { return printf("%llu\n", u); }
inline int outpLLI(long long int lli) { return printf("%lld\n", lli); }
inline void outpI(int a) {
  char c;
  char snum[20];
  int i = 0;
  int sign = 0;
  if (a < 0) sign = 1;
  a = abs(a);
  do {
    snum[i++] = a % 10 + 48;
    a = a / 10;
  } while (a != 0);
  i = i - 1;
  if (sign) putchar('-');
  while (i >= 0) putchar(snum[i--]);
  putchar('\n');
}
inline void outpI2(int a, int b) {
  printf("%d ", a);
  outpI(b);
}
inline int outpS(char *s) { return printf("%s\n", s); }
template <typename T1>
void QL_swap(T1 &x, T1 &y) {
  T1 tmp;
  tmp = x;
  x = y;
  y = tmp;
}
template <typename T1>
T1 gcd(T1 a, T1 b) {
  if (!b)
    return a;
  else
    return gcd(b, a % b);
}
long double euclideanDist(int x1, int y1, int x2, int y2) {
  return sqrt((x1 - x2) * (x1 - x2) / 1. + (y1 - y2) * (y1 - y2) / 1.);
}
}  // namespace QL_Bare_Minimum
}  // namespace QoE_Library
using namespace QoE_Library::QL_Bare_Minimum;
bool revCmp(int a, int b) { return a > b; }
int main() {
  double n, V, a[100], b[100];
  double d = 1000000000.;
  cin >> n >> V;
  int tot = 0;
  for (int i = (0); i < (n); i = i + (1)) {
    cin >> a[i];
  }
  for (int i = (0); i < (n); i = i + (1)) {
    cin >> b[i];
  }
  for (int i = (0); i < (n); i = i + (1)) {
    tot += a[i];
    d = min(d, b[i] / a[i]);
  }
  cout << setprecision(6) << fixed;
  cout << min(V, d * tot);
}