#include <cstdio>

 #include <cstring>

 #include <iostream>

 #define N 1001

 #define max(x, y) ((x) > (y) ? (x) : (y))

 int n, m, cnt, ans;

 int a[N], sum[N], head[N], to[N << ], val[N << ], next[N << ];

 bool vis[N];

 inline int read()

 {

     int x = , f = ;

     char ch = getchar();

     for(; !isdigit(ch); ch = getchar()) if(ch == '-') f = -;

     for(; isdigit(ch); ch = getchar()) x = (x << ) + (x << ) + ch - '';

     return x * f;

 }

 inline void add(int x, int y, int z)

 {

     to[cnt] = y;

     val[cnt] = z;

     next[cnt] = head[x];

     head[x] = cnt++;

 }

 inline void dfs(int u, int x)

 {

     int i, v;

     vis[u] = ;

     for(i = head[u]; i ^ -; i = next[i])

     {

         v = to[i];

         if(!vis[v])

         {

             dfs(v, x);

             if(val[i] <= x)

             {

                 if(val[i] < sum[v]) sum[u] += val[i];

                 else sum[u] += sum[v];

             }

             else sum[u] += sum[v];

         }

     }

 }

 inline bool check(int x)

 {

     memset(vis, , sizeof(vis));

     memset(sum, , sizeof(sum));

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

         if(a[i] == )

             sum[i] = m + ;

     dfs(, x);

     return sum[] <= m;

 }

 int main()

 {

     int i, x, y, z, mid;

     while()

     {

         cnt = ;

         n = read();

         m = read();

         if(!n && !m) break;

         memset(a, , sizeof(a));

         memset(head, -, sizeof(head));

         for(i = ; i < n; i++)

         {

             a[x = read()]++;

             a[y = read()]++;

             z = read();

             add(x, y, z);

             add(y, x, z);

         }

         x = , y = m, ans = -;

         while(x <= y)

         {

             mid = (x + y) >> ;

             if(check(mid)) ans = mid, y = mid - ;

             else x = mid + ;

         }

         printf("%d\n", ans);

     }

     return ;

 }