Problem: A chip was placed on a field with coordinate system onto point (0, 0).

Every second the chip moves randomly. If the chip is currently at a point (x, y), after a second it moves to the point (x - 1, y) with probability p1, to the point (x, y - 1) with probability p2, to the point (x + 1, y) with probability p3 and to the point (x, y + 1) with probability p4. It's guaranteed that p1 + p2 + p3 + p4 = 1. The moves are independent.

Find out the expected time after which chip will move away from origin at a distance greater than R (i.e. <image> will be satisfied).

Input

First line contains five integers R, a1, a2, a3 and a4 (0 ≤ R ≤ 50, 1 ≤ a1, a2, a3, a4 ≤ 1000).

Probabilities pi can be calculated using formula <image>.

Output

It can be shown that answer for this problem is always a rational number of form <image>, where <image>.

Print P·Q - 1 modulo 109 + 7. 

Examples

Input

0 1 1 1 1


Output

1

Input

1 1 1 1 1


Output

666666674

Input

1 1 2 1 2


Output

538461545

Note

In the first example initially the chip is located at a distance 0 from origin. In one second chip will move to distance 1 is some direction, so distance to origin will become 1.

Answers to the second and the third tests: <image> and <image>.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const int MAXN = 8005;
const int MAXM = 120;
const int MAXR = 60;
const int P = 1e9 + 7;
template <typename T>
void chkmax(T &x, T y) {
  x = max(x, y);
}
template <typename T>
void chkmin(T &x, T y) {
  x = min(x, y);
}
template <typename T>
void read(T &x) {
  x = 0;
  int f = 1;
  char c = getchar();
  for (; !isdigit(c); c = getchar())
    if (c == '-') f = -f;
  for (; isdigit(c); c = getchar()) x = x * 10 + c - '0';
  x *= f;
}
template <typename T>
void write(T x) {
  if (x < 0) x = -x, putchar('-');
  if (x > 9) write(x / 10);
  putchar(x % 10 + '0');
}
template <typename T>
void writeln(T x) {
  write(x);
  puts("");
}
int power(int x, int y) {
  if (y == 0) return 1;
  int tmp = power(x, y / 2);
  if (y % 2 == 0)
    return 1ll * tmp * tmp % P;
  else
    return 1ll * tmp * tmp % P * x % P;
}
int n, p[5], point[MAXM][MAXM], a[MAXN][MAXN];
int main() {
  int r;
  read(r);
  for (int i = 1; i <= 4; i++) {
    read(p[i]);
    p[0] += p[i];
  }
  for (int i = 1; i <= 4; i++) p[i] = 1ll * p[i] * power(p[0], P - 2) % P;
  for (int i = -r; i <= r; i++)
    for (int j = -r; j <= r; j++) {
      int tmp = i * i + j * j;
      if (tmp <= r * r) point[i + MAXR][j + MAXR] = ++n;
    }
  for (int i = -r + MAXR; i <= r + MAXR; i++)
    for (int j = -r + MAXR; j <= r + MAXR; j++) {
      if (point[i][j] == 0) continue;
      int tmp = point[i][j];
      a[tmp][tmp] = P - 1;
      a[tmp][n + 1] = P - 1;
      if (point[i - 1][j] != 0) a[tmp][point[i - 1][j]] = p[1];
      if (point[i][j - 1] != 0) a[tmp][point[i][j - 1]] = p[2];
      if (point[i + 1][j] != 0) a[tmp][point[i + 1][j]] = p[3];
      if (point[i][j + 1] != 0) a[tmp][point[i][j + 1]] = p[4];
    }
  for (int i = 1; i <= n; i++) {
    for (int j = i; j <= n + 1; j++)
      if (a[j][i] != 0) {
        swap(a[i], a[j]);
        break;
      }
    int top = 0;
    static int q[MAXN];
    for (int j = 1; j <= n + 1; j++)
      if (a[i][j] != 0) q[++top] = j;
    int inv = power(a[i][i], P - 2);
    for (int j = 1; j <= top; j++) a[i][q[j]] = 1ll * a[i][q[j]] * inv % P;
    for (int j = i + 1; j <= n; j++) {
      if (a[j][i] == 0) continue;
      int tmp = a[j][i];
      for (int k = 1; k <= top; k++)
        a[j][q[k]] = (a[j][q[k]] - 1ll * tmp * a[i][q[k]] % P + P) % P;
    }
  }
  for (int i = n; i >= 1; i--) {
    for (int j = i + 1; j <= n; j++)
      a[i][n + 1] = (a[i][n + 1] - 1ll * a[j][0] * a[i][j] % P + P) % P;
    a[i][0] = 1ll * a[i][n + 1] * power(a[i][i], P - 2) % P;
    if (i == point[MAXR][MAXR]) {
      writeln(a[i][0]);
      return 0;
    }
  }
  return 0;
}