glfwSetInputMode to GLFW_CURSOR_DISABLED after setting a cursor using glfwSetCursor does not hide the cursor

#include <GLFW/glfw3.h>

void key_callback(GLFWwindow* window, int key, int scancode, int action, int mods)
{
    if (action == GLFW_PRESS) return;

    if (key == GLFW_KEY_F1) {
        glfwSetInputMode(window, GLFW_CURSOR, GLFW_CURSOR_NORMAL);
        GLFWcursor* cursor = glfwCreateStandardCursor(GLFW_ARROW_CURSOR);
        glfwSetCursor(window, cursor);
    } else if (key == GLFW_KEY_F2) {
        glfwSetInputMode(window, GLFW_CURSOR, GLFW_CURSOR_DISABLED);
    }
}

int main(void)
{
    GLFWwindow* window;

    if (!glfwInit()) {
        return -1;
    }

    window = glfwCreateWindow(640, 480, "Hello World", NULL, NULL);
    if (!window) {
        glfwTerminate();
        return -1;
    }

    glfwMakeContextCurrent(window);
    glfwSetKeyCallback(window, key_callback);

    while (!glfwWindowShouldClose(window)) {
        glClear(GL_COLOR_BUFFER_BIT);
        glfwSwapBuffers(window);
        glfwPollEvents();
    }

    glfwTerminate();
    return 0;
}