Fox Ciel safely returned to her castle, but there was something wrong with the security system of the castle: sensors attached in the castle were covering her.

Ciel is at point (1, 1) of the castle now, and wants to move to point (*n*, *n*), which is the position of her room. By one step, Ciel can move from point (*x*, *y*) to either (*x* + 1, *y*) (rightward) or (*x*, *y* + 1) (upward).

In her castle, *c*<sup class="upper-index">2</sup> sensors are set at points (*a* + *i*, *b* + *j*) (for every integer *i* and *j* such that: 0 ≤ *i* &lt; *c*, 0 ≤ *j* &lt; *c*).

Each sensor has a count value and decreases its count value every time Ciel moves. Initially, the count value of each sensor is *t*. Every time Ciel moves to point (*x*, *y*), the count value of a sensor at point (*u*, *v*) decreases by (|*u* - *x*| + |*v* - *y*|). When the count value of some sensor becomes strictly less than 0, the sensor will catch Ciel as a suspicious individual!

Determine whether Ciel can move from (1, 1) to (*n*, *n*) without being caught by a sensor, and if it is possible, output her steps. Assume that Ciel can move to every point even if there is a censor on the point.
In the first line there are five integers *n*, *t*, *a*, *b*, *c* (2 ≤ *n* ≤ 2·10<sup class="upper-index">5</sup>,  0 ≤ *t* ≤ 10<sup class="upper-index">14</sup>,  1 ≤ *a* ≤ *n* - *c* + 1,  1 ≤ *b* ≤ *n* - *c* + 1,  1 ≤ *c* ≤ *n*).

Please do not use the %lld specificator to read or write 64-bit integers in C++. It is preferred to use the cin stream (also you may use the %I64d specificator).
The answers for the first sample and the second sample are shown on the picture:
print("_RANDOM_GUESS_1689177516.180588")# 1689177516.1806028