Death Star 2#4377
A long time ago in a galaxy far, far away…
The battle space station "Death Star" was designed even before the Clone Wars. Many years later, it was given to the Empire to control the Outer Rim Territories. The "Death Star" was about miles in diameter, was equipped with a graviton gun capable of destroying whole planets, and could carry a few thousand space fighters on board. The "Death Star" was meant to terrify the population and to absolutely exclude any possibility of resistance to the power of the Empire.
After the first "Death Star" was destroyed by the rebels, construction of a new, even more deadly model began. The new model, like the first one, has a spherical shape and can move translationally in -dimensional space. It is equipped with firmly anchored krypton engines. If the -th engine is provided with units of energy, its contribution to the -th coordinate of the jet thrust vector will be equal to A_{ij} \cdot X. Note that the engines are bidirectional: supplying a negative means using it to thrust in the opposite direction with units of energy. The resulting jet thrust vector is equal to the sum of the contributions from each of the engines.
Before the movement begins, a special navigational module calculates the required coordinates of the jet thrust vector (b_1, b_2, , b_N). Your program should calculate how many units of energy should be provided to each of the engines so that the length of the vector difference between the resulting jet thrust and the required jet thrust is minimized. If the answer is ambiguous, the sum of the squares of the quantities of energy provided to the engines should also be minimized.
The first line contains two integers and separated by a space (1 \leq N, M \leq 100). The following lines contain numbers each, representing the matrix A_{ij}. The last line contains numbers b_j — the coordinates of the required jet thrust vector. All A_{ij} and b_j are integers with absolute values not exceeding .
Output real numbers X_1, \dots, X_M precise to digits after the decimal point. X_i should be equal to the quantity of energy provided to the -th engine. If there is more than one answer, you may output any one.
Ejemplo 1