#include <cstdio>

 #include <iostream>

 #include <cmath>

 #include <cstring>

 using namespace std;

 const int MAXN = ;

 const double PI = acos(-1.0);

 int a[MAXN], d[MAXN], n, c;

 struct node

 {

     double x, y;

     int lazy;

 };

 node tree[MAXN << ];

 double trans(int d) { return (double)d * PI / 180.0; }

 void rotate(double & x, double & y, int dx)

 {

     double tx = x * cos(trans(dx)) - y * sin(trans(dx));

     double ty = y * cos(trans(dx)) + x * sin(trans(dx));

     x = tx; y = ty;

 }

 void pushdown(int num)

 {

     if (!tree[num].lazy) return;

     int tmp = tree[num].lazy;

     rotate(tree[num << ].x, tree[num << ].y, tmp);

     rotate(tree[num <<  | ].x, tree[num <<  | ].y, tmp);

     tree[num << ].lazy += tmp;

     tree[num <<  | ].lazy += tmp;

     tree[num].lazy = ;

 }

 void pushup(int num)

 {

     tree[num].x = tree[num << ].x + tree[num <<  | ].x;

     tree[num].y = tree[num << ].y + tree[num <<  | ].y;

 }

 void build(int num, int l, int r)

 {

     if (l == r) { tree[num].y = a[r]; return; }

     int m = l + r >> ;

     build(num << , l, m);

     build(num <<  | , m + , r);

     pushup(num);

 }

 void update(int num, int l, int r, int x, int y, int dx)

 {

     if (x <= l && y >= r)

     {

         rotate(tree[num].x, tree[num].y, dx);

         tree[num].lazy += dx;

         return;

     }

     int m = l + r >> ;

     pushdown(num);

     if (x <= m) update(num << , l, m, x, y, dx);

     if (y >= m + ) update(num <<  | , m + , r, x, y, dx);

     pushup(num);

 }

 int main()

 {

     while (scanf("%d %d", &n, &c) != EOF)

     {

         for (int i = ; i <= n * ; i++) { tree[i].x = tree[i].y = ; tree[i].lazy = ; }

         for (int i = ; i <= n; i++) scanf("%d", &a[i]);

         for (int i = ; i < n; i++) d[i] = ;

         build(, , n);

         int x, y;

         for (int i = ; i < c; i++)

         {

             scanf("%d %d", &x, &y);

             int dx = y - d[x];

             d[x] = y;

             update(, , n, x + , n, dx);

             printf("%.2f %.2f\n", tree[].x, tree[].y);

         }

         puts("");

     }

     return ;

 }